Solve 5x^2+20x-2

$$5 { x }^{ 2 } +20x-2$$

Factor

$$5\left(x-\left(-\frac{\sqrt{110}}{5}-2\right)\right)\left(x-\left(\frac{\sqrt{110}}{5}-2\right)\right)$$

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.

$$5x^{2}+20x-2=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}-4\times 5\left(-2\right)}}{2\times 5}$$

Square 20.

$$x=\frac{-20±\sqrt{400-4\times 5\left(-2\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-20±\sqrt{400-20\left(-2\right)}}{2\times 5}$$

Multiply -20 times -2.

$$x=\frac{-20±\sqrt{400+40}}{2\times 5}$$

Add 400 to 40.

$$x=\frac{-20±\sqrt{440}}{2\times 5}$$

Take the square root of 440.

$$x=\frac{-20±2\sqrt{110}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-20±2\sqrt{110}}{10}$$

Now solve the equation x=\frac{-20±2\sqrt{110}}{10} when ± is plus. Add -20 to 2\sqrt{110}.

$$x=\frac{2\sqrt{110}-20}{10}$$

Divide -20+2\sqrt{110} by 10.

$$x=\frac{\sqrt{110}}{5}-2$$

Now solve the equation x=\frac{-20±2\sqrt{110}}{10} when ± is minus. Subtract 2\sqrt{110} from -20.

$$x=\frac{-2\sqrt{110}-20}{10}$$

Divide -20-2\sqrt{110} by 10.

$$x=-\frac{\sqrt{110}}{5}-2$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -2+\frac{\sqrt{110}}{5} for x_{1} and -2-\frac{\sqrt{110}}{5} for x_{2}.

$$5x^{2}+20x-2=5\left(x-\left(\frac{\sqrt{110}}{5}-2\right)\right)\left(x-\left(-\frac{\sqrt{110}}{5}-2\right)\right)$$

Evaluate

$$5x^{2}+20x-2$$