Solve x^2-x-8+0

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

Factor

$$\left(x-\frac{1-\sqrt{33}}{2}\right)\left(x-\frac{\sqrt{33}+1}{2}\right)$$

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.

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

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-8\right)}}{2}$$

Multiply -4 times -8.

$$x=\frac{-\left(-1\right)±\sqrt{1+32}}{2}$$

Add 1 to 32.

$$x=\frac{-\left(-1\right)±\sqrt{33}}{2}$$

The opposite of -1 is 1.

$$x=\frac{1±\sqrt{33}}{2}$$

Now solve the equation x=\frac{1±\sqrt{33}}{2} when ± is plus. Add 1 to \sqrt{33}.

$$x=\frac{\sqrt{33}+1}{2}$$

Now solve the equation x=\frac{1±\sqrt{33}}{2} when ± is minus. Subtract \sqrt{33} from 1.

$$x=\frac{1-\sqrt{33}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1+\sqrt{33}}{2} for x_{1} and \frac{1-\sqrt{33}}{2} for x_{2}.

$$x^{2}-x-8=\left(x-\frac{\sqrt{33}+1}{2}\right)\left(x-\frac{1-\sqrt{33}}{2}\right)$$

Evaluate

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

Solution Steps

Add -8 and 0 to get -8.

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