Question

What number needs to be added to both sides of the equation in order to complete the square? x ^2+16x=18 Enter your answers in the boxes.

Answer 1

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

x ^2+16x=18

In completing the square , we take the coefficient of x and divide it by 2

Then square it and add it on both sides.

The coefficient of x is 16

Half of 16 is 8

Then we square it .
`(8)^2 = 64`

Add 64 on both sides

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

Now we factor x^2 + 16x+64

`(x+8)(x+8)=18+64`

`(x+8)^2=82`

so 64 is added to both sides of the equation in order to complete the square.