Solve 5x+2x^2-64=

$$5 x + 2 x ^ { 2 } - 64 =$$

Factor

$$2\left(x-\frac{-\sqrt{537}-5}{4}\right)\left(x-\frac{\sqrt{537}-5}{4}\right)$$

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.

$$2x^{2}+5x-64=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\times 2\left(-64\right)}}{2\times 2}$$

Square 5.

$$x=\frac{-5±\sqrt{25-4\times 2\left(-64\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-5±\sqrt{25-8\left(-64\right)}}{2\times 2}$$

Multiply -8 times -64.

$$x=\frac{-5±\sqrt{25+512}}{2\times 2}$$

Add 25 to 512.

$$x=\frac{-5±\sqrt{537}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-5±\sqrt{537}}{4}$$

Now solve the equation x=\frac{-5±\sqrt{537}}{4} when ± is plus. Add -5 to \sqrt{537}.

$$x=\frac{\sqrt{537}-5}{4}$$

Now solve the equation x=\frac{-5±\sqrt{537}}{4} when ± is minus. Subtract \sqrt{537} from -5.

$$x=\frac{-\sqrt{537}-5}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5+\sqrt{537}}{4} for x_{1} and \frac{-5-\sqrt{537}}{4} for x_{2}.

$$2x^{2}+5x-64=2\left(x-\frac{\sqrt{537}-5}{4}\right)\left(x-\frac{-\sqrt{537}-5}{4}\right)$$

Evaluate

$$2x^{2}+5x-64$$