Question

What number must you add to complete the square? x2 + 12x = 40

Answer 1

x² + 12x = 40
x² + 12x + (6)² = 40 + (6)²
x² + 12x + 36 = 40 + 36
(x + 6)² = 76

Answer: 36 must be added to both sides to complete the square.

Answer 2

36 should be added to make the left side a perfect square.

Explanation:

We know that
`a^(2) +2ab+b^(2) =(a+b)^(2)`

If we compare the first two terms of the left side with
`x^(2) +12x`, we get,

a = x,

2ab = 12x

But since a = x,

2xb = 12x

Cancel x both sides and divide both sides by 2.

b = 6

So,
`b^(2) =6^(2) =36` should be added to the left side to make it a perfect square.

`x^(2) +12x+36=40+36`

`(x+6)^(2) =76`