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x^{2}+2x-8=0
Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x+4.
a+b=2 ab=-8
To solve the equation, factor x^{2}+2x-8 using formula x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). To find a and b, set up a system to be solved.
-1,8 -2,4
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -8.
-1+8=7 -2+4=2
Calculate the sum for each pair.
a=-2 b=4
The solution is the pair that gives sum 2.
\left(x-2\right)\left(x+4\right)
Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.
x=2 x=-4
To find equation solutions, solve x-2=0 and x+4=0.
x=2
Variable x cannot be equal to -4.
x^{2}+2x-8=0
Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x+4.
a+b=2 ab=1\left(-8\right)=-8
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx-8. To find a and b, set up a system to be solved.
-1,8 -2,4
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -8.
-1+8=7 -2+4=2
Calculate the sum for each pair.
a=-2 b=4
The solution is the pair that gives sum 2.
\left(x^{2}-2x\right)+\left(4x-8\right)
Rewrite x^{2}+2x-8 as \left(x^{2}-2x\right)+\left(4x-8\right).
x\left(x-2\right)+4\left(x-2\right)
Factor out x in the first and 4 in the second group.
\left(x-2\right)\left(x+4\right)
Factor out common term x-2 by using distributive property.
x=2 x=-4
To find equation solutions, solve x-2=0 and x+4=0.
x=2
Variable x cannot be equal to -4.
x^{2}+2x-8=0
Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x+4.
x=\frac{-2±\sqrt{2^{2}-4\left(-8\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-2±\sqrt{4-4\left(-8\right)}}{2}
Square 2.
x=\frac{-2±\sqrt{4+32}}{2}
Multiply -4 times -8.
x=\frac{-2±\sqrt{36}}{2}
Add 4 to 32.
x=\frac{-2±6}{2}
Take the square root of 36.
x=\frac{4}{2}
Now solve the equation x=\frac{-2±6}{2} when ± is plus. Add -2 to 6.
x=2
Divide 4 by 2.
x=-\frac{8}{2}
Now solve the equation x=\frac{-2±6}{2} when ± is minus. Subtract 6 from -2.
x=-4
Divide -8 by 2.
x=2 x=-4
The equation is now solved.
x=2
Variable x cannot be equal to -4.
x^{2}+2x-8=0
Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x+4.
x^{2}+2x=8
Add 8 to both sides. Anything plus zero gives itself.
x^{2}+2x+1^{2}=8+1^{2}
Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+2x+1=8+1
Square 1.
x^{2}+2x+1=9
Add 8 to 1.
\left(x+1\right)^{2}=9
Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+1\right)^{2}}=\sqrt{9}
Take the square root of both sides of the equation.
x+1=3 x+1=-3
Simplify.
x=2 x=-4
Subtract 1 from both sides of the equation.
x=2
Variable x cannot be equal to -4.