Solve 2x^2+6x-2

$$2 { x }^{ 2 } +6x-2$$

Factor

$$2\left(x-\frac{-\sqrt{13}-3}{2}\right)\left(x-\frac{\sqrt{13}-3}{2}\right)$$

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.

$$2x^{2}+6x-2=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 2\left(-2\right)}}{2\times 2}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\times 2\left(-2\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-6±\sqrt{36-8\left(-2\right)}}{2\times 2}$$

Multiply -8 times -2.

$$x=\frac{-6±\sqrt{36+16}}{2\times 2}$$

Add 36 to 16.

$$x=\frac{-6±\sqrt{52}}{2\times 2}$$

Take the square root of 52.

$$x=\frac{-6±2\sqrt{13}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-6±2\sqrt{13}}{4}$$

Now solve the equation x=\frac{-6±2\sqrt{13}}{4} when ± is plus. Add -6 to 2\sqrt{13}.

$$x=\frac{2\sqrt{13}-6}{4}$$

Divide -6+2\sqrt{13} by 4.

$$x=\frac{\sqrt{13}-3}{2}$$

Now solve the equation x=\frac{-6±2\sqrt{13}}{4} when ± is minus. Subtract 2\sqrt{13} from -6.

$$x=\frac{-2\sqrt{13}-6}{4}$$

Divide -6-2\sqrt{13} by 4.

$$x=\frac{-\sqrt{13}-3}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{13}}{2} for x_{1} and \frac{-3-\sqrt{13}}{2} for x_{2}.

$$2x^{2}+6x-2=2\left(x-\frac{\sqrt{13}-3}{2}\right)\left(x-\frac{-\sqrt{13}-3}{2}\right)$$

Evaluate

$$2\left(x^{2}+3x-1\right)$$