Skip to main content
Factor
Tick mark Image
Evaluate
Tick mark Image
Graph

Similar Problems from Web Search

Share

2x^{2}-5x-6=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(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 2\left(-6\right)}}{2\times 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(-5\right)±\sqrt{25-4\times 2\left(-6\right)}}{2\times 2}
Square -5.
x=\frac{-\left(-5\right)±\sqrt{25-8\left(-6\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{-\left(-5\right)±\sqrt{25+48}}{2\times 2}
Multiply -8 times -6.
x=\frac{-\left(-5\right)±\sqrt{73}}{2\times 2}
Add 25 to 48.
x=\frac{5±\sqrt{73}}{2\times 2}
The opposite of -5 is 5.
x=\frac{5±\sqrt{73}}{4}
Multiply 2 times 2.
x=\frac{\sqrt{73}+5}{4}
Now solve the equation x=\frac{5±\sqrt{73}}{4} when ± is plus. Add 5 to \sqrt{73}.
x=\frac{5-\sqrt{73}}{4}
Now solve the equation x=\frac{5±\sqrt{73}}{4} when ± is minus. Subtract \sqrt{73} from 5.
2x^{2}-5x-6=2\left(x-\frac{\sqrt{73}+5}{4}\right)\left(x-\frac{5-\sqrt{73}}{4}\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{73}}{4} for x_{1} and \frac{5-\sqrt{73}}{4} for x_{2}.