Solve 2x^2+x-72

$$2 { x }^{ 2 } +x-72$$

Factor

$$2\left(x-\frac{-\sqrt{577}-1}{4}\right)\left(x-\frac{\sqrt{577}-1}{4}\right)$$

Steps Using the Quadratic Formula

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.

$$2x^{2}+x-72=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\times 2\left(-72\right)}}{2\times 2}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\times 2\left(-72\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-1±\sqrt{1-8\left(-72\right)}}{2\times 2}$$

Multiply -8 times -72.

$$x=\frac{-1±\sqrt{1+576}}{2\times 2}$$

Add 1 to 576.

$$x=\frac{-1±\sqrt{577}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-1±\sqrt{577}}{4}$$

Now solve the equation x=\frac{-1±\sqrt{577}}{4} when ± is plus. Add -1 to \sqrt{577}.

$$x=\frac{\sqrt{577}-1}{4}$$

Now solve the equation x=\frac{-1±\sqrt{577}}{4} when ± is minus. Subtract \sqrt{577} from -1.

$$x=\frac{-\sqrt{577}-1}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+\sqrt{577}}{4} for x_{1} and \frac{-1-\sqrt{577}}{4} for x_{2}.

$$2x^{2}+x-72=2\left(x-\frac{\sqrt{577}-1}{4}\right)\left(x-\frac{-\sqrt{577}-1}{4}\right)$$

Evaluate

$$2x^{2}+x-72$$