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x^{2}+5x-20=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{-5±\sqrt{5^{2}-4\left(-20\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{-5±\sqrt{25-4\left(-20\right)}}{2}
Square 5.
x=\frac{-5±\sqrt{25+80}}{2}
Multiply -4 times -20.
x=\frac{-5±\sqrt{105}}{2}
Add 25 to 80.
x=\frac{\sqrt{105}-5}{2}
Now solve the equation x=\frac{-5±\sqrt{105}}{2} when ± is plus. Add -5 to \sqrt{105}.
x=\frac{-\sqrt{105}-5}{2}
Now solve the equation x=\frac{-5±\sqrt{105}}{2} when ± is minus. Subtract \sqrt{105} from -5.
x^{2}+5x-20=\left(x-\frac{\sqrt{105}-5}{2}\right)\left(x-\frac{-\sqrt{105}-5}{2}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5+\sqrt{105}}{2} for x_{1} and \frac{-5-\sqrt{105}}{2} for x_{2}.