Solve f(x)=5x^2-8-4x

$$f ( x ) = 5 x ^ { 2 } - 8 - 4 x$$

Factor

$$5\left(x-\frac{2-2\sqrt{11}}{5}\right)\left(x-\frac{2\sqrt{11}+2}{5}\right)$$

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.

$$5x^{2}-4x-8=0$$

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.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 5\left(-8\right)}}{2\times 5}$$

Square -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 5\left(-8\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-\left(-4\right)±\sqrt{16-20\left(-8\right)}}{2\times 5}$$

Multiply -20 times -8.

$$x=\frac{-\left(-4\right)±\sqrt{16+160}}{2\times 5}$$

Add 16 to 160.

$$x=\frac{-\left(-4\right)±\sqrt{176}}{2\times 5}$$

Take the square root of 176.

$$x=\frac{-\left(-4\right)±4\sqrt{11}}{2\times 5}$$

The opposite of -4 is 4.

$$x=\frac{4±4\sqrt{11}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{4±4\sqrt{11}}{10}$$

Now solve the equation x=\frac{4±4\sqrt{11}}{10} when ± is plus. Add 4 to 4\sqrt{11}.

$$x=\frac{4\sqrt{11}+4}{10}$$

Divide 4+4\sqrt{11} by 10.

$$x=\frac{2\sqrt{11}+2}{5}$$

Now solve the equation x=\frac{4±4\sqrt{11}}{10} when ± is minus. Subtract 4\sqrt{11} from 4.

$$x=\frac{4-4\sqrt{11}}{10}$$

Divide 4-4\sqrt{11} by 10.

$$x=\frac{2-2\sqrt{11}}{5}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{2+2\sqrt{11}}{5} for x_{1} and \frac{2-2\sqrt{11}}{5} for x_{2}.

$$5x^{2}-4x-8=5\left(x-\frac{2\sqrt{11}+2}{5}\right)\left(x-\frac{2-2\sqrt{11}}{5}\right)$$

Evaluate

$$5x^{2}-4x-8$$