Question

What number should be added to both sides of the equation to complete the square?

Answer 1

Given:
x² + 12x = 11

perfect square:

a² + 2ab + b²

a² = x² ⇒ x * x
2ab = 12x ⇒ 2(6)x
b² = 6² ⇒ 36

x² + 12x + 36 = 11 + 36

(x+6)(x+6) = 47

Both sides must be added with 36.

Answer 2

Answer:

36.

Step-by-step explanation:

We have been given an equation $x^2+12x=11$ and we are asked to find the number that should be added to both sides of the equation to complete the square.

To complete the square we divide the constant with x term by two and add the square of that number to both sides of equation to complete the square.

$(\frac{b}{2})^2$

We can see that constant of x term is 12, so let us divide 12 by 2.

$\frac{12^2}{2^2}$

$\frac{144}{4}$

$36$

Therefore, we should add 36 to both sides of our equation to complete the square.

After adding 36 to both sides of our equation we will get,

$x^2+12x+36=11+36$

$x^2+12x+6^2=47$

$(x+6)^2=47$