Question

Complete the square to factor X^2 +10X=-8

Answer 1

Explanation:

X² + 10x = -8

add to both side the square of half the coefficient of X which is 5²

X² + 10x + (10/2)² = -8 + (10/2)²

X² + 5² = -8 + 5²

( X + 5 )² = -8 + 25

(X + 5)² = 17

X + 5 = +- √17

Therefore, X = -5 +- √17.

X = -5 + √17 , -5 - √17.

Answer 2

Answer:
`x=√(17)-5` and
`x = -√(17)-5`

Explanation:

Alright, lets get started.

The given equation is :

`x^(2) +10x = -8`

Adding 8 in both sides, it will become

`x^(2) +10x + 8 = -8 +8`

`x^(2) +10x + 8 = 0`

To make it perfect square, we need to add 25 and subtract 25

`x^(2) +10x + 8 +25-25= 0`

`x^2+10x+25+8-25=0`

`(x+5)^2+8-25=0`

`(x+5)^2-17=0`

Adding 17 in both sides

`(x+5)^2=17`

taking square root

`x+5=√(17)`

So,

`x=√(17)-5` and
`x = -√(17)-5` .. Answer

Hope it will help :)