Solve this quadratic equation by completing the square

x^2=12x+17

Answers

Answer 1

Answer:

[tex]\large\boxed{\red{\sf x =6+\sqrt{53},6-\sqrt{53}} }[/tex]

Step-by-step explanation:

We would like to solve the given quadratic equation by completing the square method .The given equation is ;

[tex]\longrightarrow x^2=12x +17[/tex]

Subtract 12x to both sides ,

[tex]\longrightarrow x^2-12x = 17 [/tex]

Here the co-efficient of x² is already 1 . So , we shall rewrite it as ,

[tex]\longrightarrow x^2-2(6)(x) = 17 [/tex]

Add 6² on both sides ,

[tex]\longrightarrow x^2-2(6)(x) + 6^2=17+6^2 [/tex]

Now LHS is in the form of (a-b)² = a²-2ab+ ; so that ;

[tex]\longrightarrow (x -6)^2 = 17+36 [/tex]

Simplify RHS ,

[tex]\longrightarrow (x-6)^2=53 [/tex]

Put square root on both sides,

[tex]\longrightarrow (x-6) = \pm\sqrt{53}[/tex]

Add 6 on both sides,

[tex]\longrightarrow x = 6\pm\sqrt{53} [/tex]

Separate the two solutions ,

[tex]\longrightarrow \underline{\underline{x =6+\sqrt{53},6-\sqrt{53}}} [/tex]

And we are done!


Related Questions

Write 23.4571 correct to
4 significant figures

Answers

Step-by-step explanation:

23.4571

Sig Figs6

Decimals4

Scientific Notation2.34571 × 101

Words twenty-three point four five seven one

pls answer this all pls quickly now​

Answers

Answer:

1. 35 minutes

2. 12:15 p.m.

3. 110 minutes

4. 6:05 p.m.

5. 9:21 a.m.

Step-by-step explanation:

1. Subtract 2:55 from 3:30 = 35

2. Subtract 25 minutes from 12:40 = 12:15

3. Subtract 7:20 from 9:10 = 110

4. Add 35 minutes to 5:30 = 6:05

5. Subtract 33 from 9:54 = 9:21

Elsa earns $140 for working 20 hours.
What is Elsa's rate of pay for each hour she works?
A) $6.50 per hour
B) $7.00 per hour
C) $7.25 per hour
D)$8.00 per hour

Answers

Answer:

$7

Step-by-step explanation:

Suppose she is earning an equal amount for each hour she works:

$140 = 20h divide both sides by 20

$7 = 1h she earns $7 per hour

which of the following measures can have more than one value for a set of data?

A. Mean
B. median
C. mode
D.range


Answers

Answer:

C. mode

Step-by-step explanation:

The median and mean can only have one value for a given data set. The mode can have more than one value (see Mode section on previous page).

Jeff makes $30 to mow lawns plus $2 per hour. If Jeff made #38 for one lawn, how many hours did he work?​

Answers

Answer:

4 hours

Step-by-step explanation:

What I did was since he automatically makes 30 dollars when mowing lawns, you can take it away then you have 8 and divide it by 2 then get 4 hours

In
= 2n+2n²
find the first five terms

Answers

[tex]t(n) = 2 {n}^{2} + 2n [/tex]

_________________________________

[tex]t(1) = 2 ({1})^{2} + 2(1) [/tex]

[tex]t(1) = 2 \times 1 + 2 \times 1[/tex]

[tex]t(1) = 2 + 2 = 4[/tex]

##############################

[tex]t(2) = 2 ({2})^{2} + 2(2) [/tex]

[tex]t(2) = 2 \times 4 + 2 \times 2[/tex]

[tex]t(2) = 8 + 4 = 12[/tex]

##############################

[tex]t(3) = 2 ({3})^{2} + 2(3) [/tex]

[tex]t(3) = 2 \times 9 + 2 \times 3[/tex]

[tex]t(3) = 18 + 6 = 24[/tex]

##############################

[tex]t(4) = 2 ({4})^{2} + 2(4)[/tex]

[tex]t(4) = 2 \times 16 + 2 \times 4[/tex]

[tex]t(4) = 32 + 8 = 40[/tex]

##############################

[tex]t(5) = 2 ({5})^{2} + 2(5) [/tex]

[tex]t(5) = 2 \times 25 + 2 \times 5[/tex]

[tex]t(5) = 50 + 10[/tex]

[tex]t(5) = 60[/tex]

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Solve 2x + 8 + 5x - 2 = 90

Answers

Answer:

x=12

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+8+5x−2=90

Step 1: Simplify both sides of the equation.

2x+8+5x−2=90

2x+8+5x+−2=90

(2x+5x)+(8+−2)=90(Combine Like Terms)

7x+6=90

7x+6=90

Step 2: Subtract 6 from both sides.

7x+6−6=90−6

7x=84

Step 3: Divide both sides by 7.

7x7=847

x=12

The area of the garden is 96 square feet. The width of the garden is 8 feet. What is the length of fencing needed to put around the garden?

Answers

Answer:

12 ft

Step-by-step explanation:

Length = x

Area = length * width = x * 8 = 8x

so 8x = 96

x = 12 ft

By the age of 27 justin had visited 25 of the 50 states what fraction of the states had justin visited
A:2/1
B:25/50
C:1/2
D:1/3

Answers

Answer:

Answer is B

Step-by-step explanation:

Answer:

Hello...

Step-by-step explanation:

The answer is:c)1/2

25/50=5/10=1/2

HOPE IT HELPS YOU DEAR....

Assume the total cost of a tertiary education will be R75 000 when your child enters university in 18 years. You presently have R7 000 to invest. What rate of interest must you earn on your investment to cover the cost of your child’s tertiary education?

Answers

Answer: you need 5000 more

Step-by-step explanation: 70000 + 5000= 75000

A family has two cars. The first car has fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 2150 miles, for a total gas consumption of 60 gallons, How many gallons were consumed by each of the two cars that week?

Answers

Answer:

the first car has 25 gallons of gases while the second car has 35 gallons of gases

Lines M and N are parallel. Find the measure of ∠b.

Answers

Answer: C

Step-by-step explanation:

Alternate interior angles theorem

-15x+3g=9 solve for y

Answers

Answer:

its nothing bc there is no y

Step-by-step explanation:

What is the least common multiple of 4 and 12? 4 12 24 D48​

Answers

Answer:

12

Step-by-step explanation:

find the slope of the line that passes through the points A(-6,2) and B(5,-1).

A 3/11
B -3/11
C -1
D -11/3​

Answers

Answer:

[tex]\boxed{\sf{m=-\dfrac{3}{11} }}[/tex]

Step-by-step explanation:

You simply need to use a slope formula that passes through the points in order to solve this problem.

Slope:

[tex]\sf{\dfrac{Y_2-Y_1}{X_2-X_1}=\dfrac{RISE}{RUN} }[/tex]

y2=(-1)

y1=2

x2=5

x1=(-6)

Rewrite the problem down.

[tex]\sf{\dfrac{-1-2}{5-(-6)}=\dfrac{-1-2}{5+6}=\dfrac{-3}{11}=\boxed{\sf{-\dfrac{3}{11} }}}[/tex]

-3/11

Therefore, the slope is -3/11, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.


Dan drinks 6 more glasses of water than Becky.
Becky drinks 5 glasses of water.

How many glasses of water did Dan drink?

Answers

Answer:

Dan drank 11 glasses of water

Step-by-step explanation:

5 + 6 = 11

Answer:

11

Step-by-step explanation:

5+6=11

QUICKKKKKKKKKKKKKKKKKKKKKK PLSSSSSSSSSS
ILL MAKE U BRAINLYEST oops spelt it wrong anyway QUICKKKKKKKK IM ON A TIMER!!!!!!!

Answers

The answer is 2/25 (B)

Solve-3.5+4.2=?solve

Answers

7.7 the answer in 7.7 because 2+5 = 7 and 3+4= 11

Answer:

Step-by-step explanation:

  0.7

 -3.5

+ 4.2

______

The ratio of left-handed students to right-handed students in Mr. Johnson's first period class is 2: 3. If there are 30 students in this class, how many are left-handed?

Answers

12 students are left handed.

i hope this helps!:)

Answer:

12 left-handed students

Step-by-step explanation:

The ratio 2:3 indicates 2 left-handed students for every 3 right-handed students.  This means 2 left-handed students are expected for every 5 total students.  You can use this information and set up and solve the proportion 2/5 = x/30

What is the constant of proportionality?

Enter your answer in the box.

Answers

Answer:

  12

Step-by-step explanation:

The constant of proportionality is the slope of the line, the ratio of the y-coordinate to the x-coordinate.

  k = 36/3 = 12 . . . . . from the lower left point (not the origin)

__

Additional comment

This comes from the equation for a proportion:

  y = kx

Solving for k, we get ...

  k = y/x

A proportion always graphs as a line through the origin. The slope of it is k, the constant of proportionality.

Kammi wrote the numbers -3, -3.5, 4, and -4.5 in order from least to greatest. How did she write the numbers?

Answers

Since she is writing the numbers from least to greatest, they would be written like this:

-4.5, -3.5, -3, 4

The greater the negative number, the more the value decreases. Negative numbers are always less than non-negative numbers.

Kristen drinks 0.5 liter of orange juice with breakfast each day for 15 days . how many milliliters of orange juice does Kristen drink during the 15 days?​

Answers

Answer:

7500 ml

Step-by-step explanation:

first times 0.15 x 15

you get 7.5 liters during the 15 days

convert that into milliliters and its 7500ml

The value of square root of 35 is between 5 and 6. Which of the following is a more precise approximation of square root of 35?

Answers

Answer:6

Step-by-step explanation:

because [tex]\sqrt{35}[/tex] is closer to 6 than 5 and is also about 5.9...

If h(x) = 2x+3 and g(x) = 3x-2, find the value of goh(5).​

Answers

Answer:

h(x)=2x+3

g(x)=3x-2

First we will find goh(x) then we will put the value of x i.e 5.

goh(x)= 3(2x+3)-2

goh(x)=6x+9-2

goh(x)=6x+7

Now put the value of x, we get

goh(5)=6(5)+7

We get the answer 37

Step-by-step explanation:

how do i solve this can someone give me the answer

Answers

Answer:

I don't see a question, so it Imma answer how it seems.

It looks like it's B. x < -6.

(You can tell bc the circle is open and the arrow is pointing left.)

I think this is right

Step-by-step explanation:

A store sells ice cream with assorted toppings. They charge $$$3.00 for an ice cream plus $$50 cents per ounce of toppings.

How much does an ice cream cost with $$11 ounces of toppings?

Answers

Answer:

$5.50

Step-by-step explanation:

so if its $3 for an ice cream plus .50 cents per ounce all you have to do is 11 x 0.50 witch would equal $ 5.50.

If I dilate a 2x2 square by a scale factor of 3, what will be the new area?

Answers

Answer:

36 square units

Step-by-step explanation:

A 2x2 square has sides that are 2 units long.

When you dilate by a factor of 3, each side has a length 3 times the original length. 2 * 3 = 6. Each side is now 6 units long.

area = side * side = 6 units * 6 units = 36 units^2

It pays 6% interest annually for 2 years.
Liam would like to earn $750 in interest.

How much money does he need to put in?

Answers

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$750\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &2 \end{cases} \\\\\\ 750 = (P)(0.06)(2)\implies \cfrac{750}{(0.06)(2)}=P\implies 6250=P[/tex]

Drag each expression to show whether it is equivalent to 36x+9 or 9(4x−1).

Answers

Answer:

It is not equivalent.

Step-by-step explanation:

9(4x-1) simplifys out to 36x-9.

hi can youhelp me plese

Answers

The mid for this graph is where the middle for the function is and it’s y= -1
Other Questions
ideology about fidel ramos Cowboys DE Demarcus Lawrence agrees to new three-year, $40M deal Why did King George make the Proclamation of 1763? Why is there an increase in the number of people infected with the disease despite the increase in the number of vaccinated? What was En Hedu' Anna the first scientist to do? To monitor the movement of the earth. To monitor the movement of the stars and moon. To monitor the movement of the planets. To monitor the movement of the sun. After buying some lumber from your local home supply store, you realize that you need to attach a red flag from the end of the lumber because it is hanging out behind your vehicle at least ____ feet. Can someone help me with this? QUICKLY PLEASE!!18POINTS!6(3p 2) = 24 Help i need help..... All of the rocks in the world used to be _________________ rock called molten rock. Do these ratios form a proportion?$30 per 46 pounds$15 per 23 poundsYes or No At a bookstore, the cost for a novel and a magazine is $8.27. The cost for 3 novels and 5 magazines is $20.22. Which pair of equations can be used to determine n, the cost of a novel, and m, the cost of a magazine? n + 5m = 8.27 3n + m = 20.22 n + 5m = 8.27, , 3n + m = 20.22, n + m = 8.27 3n + 5m = 20.22 n + m = 8.27, , 3n + 5m = 20.22, n + m = 20.22 3n + 5m = 8.27 n + m = 20.22, , 3n + 5m = 8.27, 3n + m = 8.27 n + 5m = 20.22 what is 32123 one more thingwhat is 3,8291221 This famous painting is of General blank crossing the blank river The Steller sea lion population has been decreasing in parts of Alaska. New evidence suggests that Steller sea lions need herring as a part of their diet in order to survive. Pollock, another type of fish, also feed on herring. Which would most likely help the Steller sea lion population to increase? Which is a strategy for eating better?Eat raw nuts as snacks, reduce the amount of vegetables in meals, eat white rice instead of brown rice, fry vegetables and proteins for meals Dee is at a rehabilitation center for misusing prescription drugs. What are some ways Dee might have used these legal drugs in a harmful way in an attempt to produce another effect, rather than for their intended purpose? What are some potential negative effects Dee might have experienced due to combining drugs, such as prescription and over-the-counter drugs? PLEASE NO LINKS, NEED TODAY Can someone help me ASAP, its pretty easy Im just not sure which one because they all kinda seem like a good option. BRAINLY AND LOTSSS OF POINST IF ANSWERED FAST AND RIGHT14. Discuss the density of water? Of ice? Why is this different than would be expected?15. Why does a frost kill plants What is the solution to the equation x = 6x = 1x = 1x = 2