Solve x^2-8x++1x+8

$$x ^ { 2 } - 8 x + + 1 x + 8$$

Factor

$$\left(x-\frac{7-\sqrt{17}}{2}\right)\left(x-\frac{\sqrt{17}+7}{2}\right)$$

Steps Using the Quadratic Formula

Combine -8x and 1x to get -7x.

$$factor(x^{2}-7x+8)$$

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.

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

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.

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

Square -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 8}}{2}$$

Multiply -4 times 8.

$$x=\frac{-\left(-7\right)±\sqrt{49-32}}{2}$$

Add 49 to -32.

$$x=\frac{-\left(-7\right)±\sqrt{17}}{2}$$

The opposite of -7 is 7.

$$x=\frac{7±\sqrt{17}}{2}$$

Now solve the equation x=\frac{7±\sqrt{17}}{2} when ± is plus. Add 7 to \sqrt{17}.

$$x=\frac{\sqrt{17}+7}{2}$$

Now solve the equation x=\frac{7±\sqrt{17}}{2} when ± is minus. Subtract \sqrt{17} from 7.

$$x=\frac{7-\sqrt{17}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{7+\sqrt{17}}{2} for x_{1} and \frac{7-\sqrt{17}}{2} for x_{2}.

$$x^{2}-7x+8=\left(x-\frac{\sqrt{17}+7}{2}\right)\left(x-\frac{7-\sqrt{17}}{2}\right)$$

Evaluate

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

Solution Steps

Combine -8x and 1x to get -7x.

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