Question

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

Answer 1

Answer:

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

Step-by-step 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.

$x^{2} +12x+36=40+36$

$(x+6)^{2} =76$

Answer 2

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.