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0=x^{2}+4x-32
Use the distributive property to multiply x-4 by x+8 and combine like terms.
x^{2}+4x-32=0
Swap sides so that all variable terms are on the left hand side.
a+b=4 ab=-32
To solve the equation, factor x^{2}+4x-32 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.
-1,32 -2,16 -4,8
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 -32.
-1+32=31 -2+16=14 -4+8=4
Calculate the sum for each pair.
a=-4 b=8
The solution is the pair that gives sum 4.
\left(x-4\right)\left(x+8\right)
Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.
x=4 x=-8
To find equation solutions, solve x-4=0 and x+8=0.
0=x^{2}+4x-32
Use the distributive property to multiply x-4 by x+8 and combine like terms.
x^{2}+4x-32=0
Swap sides so that all variable terms are on the left hand side.
a+b=4 ab=1\left(-32\right)=-32
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx-32. To find a and b, set up a system to be solved.
-1,32 -2,16 -4,8
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 -32.
-1+32=31 -2+16=14 -4+8=4
Calculate the sum for each pair.
a=-4 b=8
The solution is the pair that gives sum 4.
\left(x^{2}-4x\right)+\left(8x-32\right)
Rewrite x^{2}+4x-32 as \left(x^{2}-4x\right)+\left(8x-32\right).
x\left(x-4\right)+8\left(x-4\right)
Factor out x in the first and 8 in the second group.
\left(x-4\right)\left(x+8\right)
Factor out common term x-4 by using distributive property.
x=4 x=-8
To find equation solutions, solve x-4=0 and x+8=0.
0=x^{2}+4x-32
Use the distributive property to multiply x-4 by x+8 and combine like terms.
x^{2}+4x-32=0
Swap sides so that all variable terms are on the left hand side.
x=\frac{-4±\sqrt{4^{2}-4\left(-32\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±\sqrt{16-4\left(-32\right)}}{2}
Square 4.
x=\frac{-4±\sqrt{16+128}}{2}
Multiply -4 times -32.
x=\frac{-4±\sqrt{144}}{2}
Add 16 to 128.
x=\frac{-4±12}{2}
Take the square root of 144.
x=\frac{8}{2}
Now solve the equation x=\frac{-4±12}{2} when ± is plus. Add -4 to 12.
x=4
Divide 8 by 2.
x=-\frac{16}{2}
Now solve the equation x=\frac{-4±12}{2} when ± is minus. Subtract 12 from -4.
x=-8
Divide -16 by 2.
x=4 x=-8
The equation is now solved.
0=x^{2}+4x-32
Use the distributive property to multiply x-4 by x+8 and combine like terms.
x^{2}+4x-32=0
Swap sides so that all variable terms are on the left hand side.
x^{2}+4x=32
Add 32 to both sides. Anything plus zero gives itself.
x^{2}+4x+2^{2}=32+2^{2}
Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+4x+4=32+4
Square 2.
x^{2}+4x+4=36
Add 32 to 4.
\left(x+2\right)^{2}=36
Factor x^{2}+4x+4. 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+2\right)^{2}}=\sqrt{36}
Take the square root of both sides of the equation.
x+2=6 x+2=-6
Simplify.
x=4 x=-8
Subtract 2 from both sides of the equation.