Solve for x
x=8
x=-4
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x^{2}-4x+4=36
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-4x+4-36=0
Subtract 36 from both sides.
x^{2}-4x-32=0
Subtract 36 from 4 to get -32.
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 negative, the negative number has greater absolute value than the positive. 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=-8 b=4
The solution is the pair that gives sum -4.
\left(x-8\right)\left(x+4\right)
Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.
x=8 x=-4
To find equation solutions, solve x-8=0 and x+4=0.
x^{2}-4x+4=36
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-4x+4-36=0
Subtract 36 from both sides.
x^{2}-4x-32=0
Subtract 36 from 4 to get -32.
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 negative, the negative number has greater absolute value than the positive. 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=-8 b=4
The solution is the pair that gives sum -4.
\left(x^{2}-8x\right)+\left(4x-32\right)
Rewrite x^{2}-4x-32 as \left(x^{2}-8x\right)+\left(4x-32\right).
x\left(x-8\right)+4\left(x-8\right)
Factor out x in the first and 4 in the second group.
\left(x-8\right)\left(x+4\right)
Factor out common term x-8 by using distributive property.
x=8 x=-4
To find equation solutions, solve x-8=0 and x+4=0.
x^{2}-4x+4=36
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-4x+4-36=0
Subtract 36 from both sides.
x^{2}-4x-32=0
Subtract 36 from 4 to get -32.
x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{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{-\left(-4\right)±\sqrt{16-4\left(-32\right)}}{2}
Square -4.
x=\frac{-\left(-4\right)±\sqrt{16+128}}{2}
Multiply -4 times -32.
x=\frac{-\left(-4\right)±\sqrt{144}}{2}
Add 16 to 128.
x=\frac{-\left(-4\right)±12}{2}
Take the square root of 144.
x=\frac{4±12}{2}
The opposite of -4 is 4.
x=\frac{16}{2}
Now solve the equation x=\frac{4±12}{2} when ± is plus. Add 4 to 12.
x=8
Divide 16 by 2.
x=-\frac{8}{2}
Now solve the equation x=\frac{4±12}{2} when ± is minus. Subtract 12 from 4.
x=-4
Divide -8 by 2.
x=8 x=-4
The equation is now solved.
\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=8 x=-4
Add 2 to both sides of the equation.
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