Skip to main content
$\exponential{(x)}{2} - 20 x + 36 $
Factor
Tick mark Image
Evaluate
Tick mark Image
Graph

Similar Problems from Web Search

Share

a+b=-20 ab=1\times 36=36
Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+36. To find a and b, set up a system to be solved.
-1,-36 -2,-18 -3,-12 -4,-9 -6,-6
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 36.
-1-36=-37 -2-18=-20 -3-12=-15 -4-9=-13 -6-6=-12
Calculate the sum for each pair.
a=-18 b=-2
The solution is the pair that gives sum -20.
\left(x^{2}-18x\right)+\left(-2x+36\right)
Rewrite x^{2}-20x+36 as \left(x^{2}-18x\right)+\left(-2x+36\right).
x\left(x-18\right)-2\left(x-18\right)
Factor out x in the first and -2 in the second group.
\left(x-18\right)\left(x-2\right)
Factor out common term x-18 by using distributive property.
x^{2}-20x+36=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(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 36}}{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(-20\right)±\sqrt{400-4\times 36}}{2}
Square -20.
x=\frac{-\left(-20\right)±\sqrt{400-144}}{2}
Multiply -4 times 36.
x=\frac{-\left(-20\right)±\sqrt{256}}{2}
Add 400 to -144.
x=\frac{-\left(-20\right)±16}{2}
Take the square root of 256.
x=\frac{20±16}{2}
The opposite of -20 is 20.
x=\frac{36}{2}
Now solve the equation x=\frac{20±16}{2} when ± is plus. Add 20 to 16.
x=18
Divide 36 by 2.
x=\frac{4}{2}
Now solve the equation x=\frac{20±16}{2} when ± is minus. Subtract 16 from 20.
x=2
Divide 4 by 2.
x^{2}-20x+36=\left(x-18\right)\left(x-2\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 18 for x_{1} and 2 for x_{2}.