Solve x^2+15x+8-0

$$x ^ { 2 } + 15 x + 8 - 0$$

Evaluate

$$x^{2}+15x+8$$

Solution Steps

Multiply -1 and 0 to get 0.

$$x^{2}+15x+8+0$$

Add 8 and 0 to get 8.

$$x^{2}+15x+8$$

Factor

$$\left(x-\frac{-\sqrt{193}-15}{2}\right)\left(x-\frac{\sqrt{193}-15}{2}\right)$$

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.

$$x^{2}+15x+8=0$$

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.

$$x=\frac{-15±\sqrt{15^{2}-4\times 8}}{2}$$

Square 15.

$$x=\frac{-15±\sqrt{225-4\times 8}}{2}$$

Multiply -4 times 8.

$$x=\frac{-15±\sqrt{225-32}}{2}$$

Add 225 to -32.

$$x=\frac{-15±\sqrt{193}}{2}$$

Now solve the equation x=\frac{-15±\sqrt{193}}{2} when ± is plus. Add -15 to \sqrt{193}.

$$x=\frac{\sqrt{193}-15}{2}$$

Now solve the equation x=\frac{-15±\sqrt{193}}{2} when ± is minus. Subtract \sqrt{193} from -15.

$$x=\frac{-\sqrt{193}-15}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-15+\sqrt{193}}{2} for x_{1} and \frac{-15-\sqrt{193}}{2} for x_{2}.

$$x^{2}+15x+8=\left(x-\frac{\sqrt{193}-15}{2}\right)\left(x-\frac{-\sqrt{193}-15}{2}\right)$$