Solve 2x^2+12x-30

$$2 { x }^{ 2 } +12x-30$$

Factor

$$2\left(x-\left(-2\sqrt{6}-3\right)\right)\left(x-\left(2\sqrt{6}-3\right)\right)$$

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.

$$2x^{2}+12x-30=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 2\left(-30\right)}}{2\times 2}$$

Square 12.

$$x=\frac{-12±\sqrt{144-4\times 2\left(-30\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-12±\sqrt{144-8\left(-30\right)}}{2\times 2}$$

Multiply -8 times -30.

$$x=\frac{-12±\sqrt{144+240}}{2\times 2}$$

Add 144 to 240.

$$x=\frac{-12±\sqrt{384}}{2\times 2}$$

Take the square root of 384.

$$x=\frac{-12±8\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-12±8\sqrt{6}}{4}$$

Now solve the equation x=\frac{-12±8\sqrt{6}}{4} when ± is plus. Add -12 to 8\sqrt{6}.

$$x=\frac{8\sqrt{6}-12}{4}$$

Divide -12+8\sqrt{6} by 4.

$$x=2\sqrt{6}-3$$

Now solve the equation x=\frac{-12±8\sqrt{6}}{4} when ± is minus. Subtract 8\sqrt{6} from -12.

$$x=\frac{-8\sqrt{6}-12}{4}$$

Divide -12-8\sqrt{6} by 4.

$$x=-2\sqrt{6}-3$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -3+2\sqrt{6} for x_{1} and -3-2\sqrt{6} for x_{2}.

$$2x^{2}+12x-30=2\left(x-\left(2\sqrt{6}-3\right)\right)\left(x-\left(-2\sqrt{6}-3\right)\right)$$

Evaluate

$$2\left(x^{2}+6x-15\right)$$