Solve 2x^2+8x-54

$$2 { x }^{ 2 } +8x-54$$

Factor

$$2\left(x-\left(-\sqrt{31}-2\right)\right)\left(x-\left(\sqrt{31}-2\right)\right)$$

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.

$$2x^{2}+8x-54=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 2\left(-54\right)}}{2\times 2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\times 2\left(-54\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-8±\sqrt{64-8\left(-54\right)}}{2\times 2}$$

Multiply -8 times -54.

$$x=\frac{-8±\sqrt{64+432}}{2\times 2}$$

Add 64 to 432.

$$x=\frac{-8±\sqrt{496}}{2\times 2}$$

Take the square root of 496.

$$x=\frac{-8±4\sqrt{31}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-8±4\sqrt{31}}{4}$$

Now solve the equation x=\frac{-8±4\sqrt{31}}{4} when ± is plus. Add -8 to 4\sqrt{31}.

$$x=\frac{4\sqrt{31}-8}{4}$$

Divide -8+4\sqrt{31} by 4.

$$x=\sqrt{31}-2$$

Now solve the equation x=\frac{-8±4\sqrt{31}}{4} when ± is minus. Subtract 4\sqrt{31} from -8.

$$x=\frac{-4\sqrt{31}-8}{4}$$

Divide -8-4\sqrt{31} by 4.

$$x=-\sqrt{31}-2$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -2+\sqrt{31} for x_{1} and -2-\sqrt{31} for x_{2}.

$$2x^{2}+8x-54=2\left(x-\left(\sqrt{31}-2\right)\right)\left(x-\left(-\sqrt{31}-2\right)\right)$$

Evaluate

$$2\left(x^{2}+4x-27\right)$$