Question

What number must you add to complete the square?
x^2 + 10x = 8

A. 25
B. 10
C. 5
D. 15

Answer 1

To complete the square:

1) Take the coefficient of the 'x' term --> 10 here
2) Divide it by 2 --> So (10/2) = 5
3) Square the result --> So 5^2 = 25
4) Add it to both sides of the equation

Meaning your answer is...?

Answer 2

25x^2+10x=32?

Answer 3

so the answer is either a or c?

Answer 4

*my mind is broken whilst doing math*

Answer 5

Not quite. Why did you combine the 25 and the x^2 term?

So the goal here is to get our equation from

\[\large x^2 + 10x = 8\]

To something that looks like

\[\large x^2 + 10x + \text{__} = c\]

Which will ultimately factor into

\[\large (x + \text{something})^2 = c\]

Answer 6

Uhh

Answer 7

So here...from the beginning

\[\large x^2 + 10x = 8\]

We take the coefficient of the 'x term and divide it by 2...and the square the result
--> (10/2)^2 = 25

Now we add that to both sides of the equation

\[\large x^2 + 10x + 25 = 8 + 25\]
\[\large x^2 + 10x + 25 = 32\]

Answer 8

So that is it...in order to complete the square...we just needed to add 25 to the equation

Answer 9

Oh! Okay, so 25 is the perfect square, but 5 is the square itself.

Answer 10

Exactly!

Answer 11

THANK YOU SO MUCH!

Answer 12

Not a problem!

Answer 13

Im getting ready to post another question... lol
I have so many!