Solve -7+8x^2-4x

$$- 7 + 8 x ^ { 2 } - 4 x$$

Factor

$$8\left(x-\frac{1-\sqrt{15}}{4}\right)\left(x-\frac{\sqrt{15}+1}{4}\right)$$

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.

$$8x^{2}-4x-7=0$$

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.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 8\left(-7\right)}}{2\times 8}$$

Square -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 8\left(-7\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-\left(-4\right)±\sqrt{16-32\left(-7\right)}}{2\times 8}$$

Multiply -32 times -7.

$$x=\frac{-\left(-4\right)±\sqrt{16+224}}{2\times 8}$$

Add 16 to 224.

$$x=\frac{-\left(-4\right)±\sqrt{240}}{2\times 8}$$

Take the square root of 240.

$$x=\frac{-\left(-4\right)±4\sqrt{15}}{2\times 8}$$

The opposite of -4 is 4.

$$x=\frac{4±4\sqrt{15}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{4±4\sqrt{15}}{16}$$

Now solve the equation x=\frac{4±4\sqrt{15}}{16} when ± is plus. Add 4 to 4\sqrt{15}.

$$x=\frac{4\sqrt{15}+4}{16}$$

Divide 4+4\sqrt{15} by 16.

$$x=\frac{\sqrt{15}+1}{4}$$

Now solve the equation x=\frac{4±4\sqrt{15}}{16} when ± is minus. Subtract 4\sqrt{15} from 4.

$$x=\frac{4-4\sqrt{15}}{16}$$

Divide 4-4\sqrt{15} by 16.

$$x=\frac{1-\sqrt{15}}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1+\sqrt{15}}{4} for x_{1} and \frac{1-\sqrt{15}}{4} for x_{2}.

$$8x^{2}-4x-7=8\left(x-\frac{\sqrt{15}+1}{4}\right)\left(x-\frac{1-\sqrt{15}}{4}\right)$$

Evaluate

$$8x^{2}-4x-7$$