Question

What number needs to be added to both sides of the equation in order to complete the square?

x^2+16x=18

x^2+16x+___ =18+____

Answer 1

64

Step-by-step explanation:64

To complete the square for the equation x^2 + 16x = 18, you need to add a constant to both sides of the equation such that the left side becomes a perfect square trinomial.

Start by adding half of the coefficient of the linear term (16x) squared to both sides of the equation

Answer 2

64.

Explanation:

We have been given an equation
`x^2+16x=18`. We are asked to complete the square for the given equation.

We know that to complete a square, we add half the square of x term to both sides of equation to complete square.

We can see that coefficient of x term is 16.

`((b)/(2))^2=((16)/(2))^2=8^2=64`

Add 64 on both sides of equation:

`x^2+16x+64=18+64`

`x^2+2*8x+8^2=82`

`(x+8)^2=82`

Therefore, 64 needs to be added to both sides of the equation in order to complete the square.