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x^{2}+10x+25-36=0
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.
x^{2}+10x-11=0
Subtract 36 from 25 to get -11.
a+b=10 ab=-11
To solve the equation, factor x^{2}+10x-11 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.
a=-1 b=11
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. The only such pair is the system solution.
\left(x-1\right)\left(x+11\right)
Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.
x=1 x=-11
To find equation solutions, solve x-1=0 and x+11=0.
x^{2}+10x+25-36=0
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.
x^{2}+10x-11=0
Subtract 36 from 25 to get -11.
a+b=10 ab=1\left(-11\right)=-11
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx-11. To find a and b, set up a system to be solved.
a=-1 b=11
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. The only such pair is the system solution.
\left(x^{2}-x\right)+\left(11x-11\right)
Rewrite x^{2}+10x-11 as \left(x^{2}-x\right)+\left(11x-11\right).
x\left(x-1\right)+11\left(x-1\right)
Factor out x in the first and 11 in the second group.
\left(x-1\right)\left(x+11\right)
Factor out common term x-1 by using distributive property.
x=1 x=-11
To find equation solutions, solve x-1=0 and x+11=0.
x^{2}+10x+25-36=0
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.
x^{2}+10x-11=0
Subtract 36 from 25 to get -11.
x=\frac{-10±\sqrt{10^{2}-4\left(-11\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 10 for b, and -11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-10±\sqrt{100-4\left(-11\right)}}{2}
Square 10.
x=\frac{-10±\sqrt{100+44}}{2}
Multiply -4 times -11.
x=\frac{-10±\sqrt{144}}{2}
Add 100 to 44.
x=\frac{-10±12}{2}
Take the square root of 144.
x=\frac{2}{2}
Now solve the equation x=\frac{-10±12}{2} when ± is plus. Add -10 to 12.
x=1
Divide 2 by 2.
x=-\frac{22}{2}
Now solve the equation x=\frac{-10±12}{2} when ± is minus. Subtract 12 from -10.
x=-11
Divide -22 by 2.
x=1 x=-11
The equation is now solved.
x^{2}+10x+25-36=0
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.
x^{2}+10x-11=0
Subtract 36 from 25 to get -11.
x^{2}+10x=11
Add 11 to both sides. Anything plus zero gives itself.
x^{2}+10x+5^{2}=11+5^{2}
Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+10x+25=11+25
Square 5.
x^{2}+10x+25=36
Add 11 to 25.
\left(x+5\right)^{2}=36
Factor x^{2}+10x+25. 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+5\right)^{2}}=\sqrt{36}
Take the square root of both sides of the equation.
x+5=6 x+5=-6
Simplify.
x=1 x=-11
Subtract 5 from both sides of the equation.