Question

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

Answer 1

Answer: $x=\sqrt{17}-5$ and $x = -\sqrt{17}-5$

Step-by-step 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

$x+5=\sqrt{17}$

So,

$x=\sqrt{17}-5$ and $x = -\sqrt{17}-5$  .. Answer

Hope it will help :)

Answer 2

Answer:

Step-by-step 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.