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a+b=-6 ab=1\left(-55\right)=-55
Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-55. To find a and b, set up a system to be solved.
1,-55 5,-11
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 -55.
1-55=-54 5-11=-6
Calculate the sum for each pair.
a=-11 b=5
The solution is the pair that gives sum -6.
\left(x^{2}-11x\right)+\left(5x-55\right)
Rewrite x^{2}-6x-55 as \left(x^{2}-11x\right)+\left(5x-55\right).
x\left(x-11\right)+5\left(x-11\right)
Factor out x in the first and 5 in the second group.
\left(x-11\right)\left(x+5\right)
Factor out common term x-11 by using distributive property.
x^{2}-6x-55=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-55\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-\left(-6\right)±\sqrt{36-4\left(-55\right)}}{2}
Square -6.
x=\frac{-\left(-6\right)±\sqrt{36+220}}{2}
Multiply -4 times -55.
x=\frac{-\left(-6\right)±\sqrt{256}}{2}
Add 36 to 220.
x=\frac{-\left(-6\right)±16}{2}
Take the square root of 256.
x=\frac{6±16}{2}
The opposite of -6 is 6.
x=\frac{22}{2}
Now solve the equation x=\frac{6±16}{2} when ± is plus. Add 6 to 16.
x=11
Divide 22 by 2.
x=-\frac{10}{2}
Now solve the equation x=\frac{6±16}{2} when ± is minus. Subtract 16 from 6.
x=-5
Divide -10 by 2.
x^{2}-6x-55=\left(x-11\right)\left(x-\left(-5\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 11 for x_{1} and -5 for x_{2}.
x^{2}-6x-55=\left(x-11\right)\left(x+5\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.