Answer: [tex]x=\sqrt{17}-5[/tex] and [tex]x = -\sqrt{17}-5[/tex]
Step-by-step explanation:
Alright, lets get started.
The given equation is :
[tex]x^{2} +10x = -8[/tex]
Adding 8 in both sides, it will become
[tex]x^{2} +10x + 8 = -8 +8[/tex]
[tex]x^{2} +10x + 8 = 0[/tex]
To make it perfect square, we need to add 25 and subtract 25
[tex]x^{2} +10x + 8 +25-25= 0[/tex]
[tex]x^2+10x+25+8-25=0[/tex]
[tex](x+5)^2+8-25=0[/tex]
[tex](x+5)^2-17=0[/tex]
Adding 17 in both sides
[tex](x+5)^2=17[/tex]
taking square root
[tex]x+5=\sqrt{17}[/tex]
So,
[tex]x=\sqrt{17}-5[/tex] and [tex]x = -\sqrt{17}-5[/tex] .. Answer
Hope it will help :)
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.
