Solve x^2+16+15x

$$x ^ { 2 } + 16 + 15 x$$

Factor

$$\left(x-\frac{-\sqrt{161}-15}{2}\right)\left(x-\frac{\sqrt{161}-15}{2}\right)$$

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.

$$x^{2}+15x+16=0$$

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.

$$x=\frac{-15±\sqrt{15^{2}-4\times 16}}{2}$$

Square 15.

$$x=\frac{-15±\sqrt{225-4\times 16}}{2}$$

Multiply -4 times 16.

$$x=\frac{-15±\sqrt{225-64}}{2}$$

Add 225 to -64.

$$x=\frac{-15±\sqrt{161}}{2}$$

Now solve the equation x=\frac{-15±\sqrt{161}}{2} when ± is plus. Add -15 to \sqrt{161}.

$$x=\frac{\sqrt{161}-15}{2}$$

Now solve the equation x=\frac{-15±\sqrt{161}}{2} when ± is minus. Subtract \sqrt{161} from -15.

$$x=\frac{-\sqrt{161}-15}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-15+\sqrt{161}}{2} for x_{1} and \frac{-15-\sqrt{161}}{2} for x_{2}.

$$x^{2}+15x+16=\left(x-\frac{\sqrt{161}-15}{2}\right)\left(x-\frac{-\sqrt{161}-15}{2}\right)$$

Evaluate

$$x^{2}+15x+16$$