Question

What number must you add to complete the square x^-8x=39

Answer 1

The number must be added to complete the square is 16

Explanation:

It is given that,

x^2 - 8x = 39 ------(1)

The quadratic equation is of the form ax^2 + bx + c =0

To complete the square we have to add (b/2)^2 and subtract (b/2)^2

Therefore the eq (1) becomes

here b= -8, so we have to add (8/2)^2 = 4^2 = 16

Therefore the number is 16

To find x

x^2 - 8x = 39

Add 16 to both sides

x^2 - 8x +16 = 39 + 16

(x - 4)^2 = 55

x - 4 = √55

x = √55 -4

Answer 2

Given equation:
`x^2-8x =39`

when we complete the square , we take half of the value of 8 , then square it, and added to the left sides, we get;

`x^2-8x+4^2 = 39 +4^2`

∵8 is the value
`((8)/(2))^2`

Notice that, we add this both sides so that it maintains the equality.

then;

`x^2-8x+4^2 = 39 +4^2`

`(x-4)^2 = 39 + 16` [
`(a-b)^2 = a^2-2ab+b^2` ]

Simplify:

`(x-4)^2 =55`

The number must be added to complete the square is,
`4^2 = 16`