Solve x^2+18x+64

$${ x }^{ 2 } +18x+64$$

Factor

$$\left(x-\left(-\sqrt{17}-9\right)\right)\left(x-\left(\sqrt{17}-9\right)\right)$$

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.

$$x^{2}+18x+64=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\times 64}}{2}$$

Square 18.

$$x=\frac{-18±\sqrt{324-4\times 64}}{2}$$

Multiply -4 times 64.

$$x=\frac{-18±\sqrt{324-256}}{2}$$

Add 324 to -256.

$$x=\frac{-18±\sqrt{68}}{2}$$

Take the square root of 68.

$$x=\frac{-18±2\sqrt{17}}{2}$$

Now solve the equation x=\frac{-18±2\sqrt{17}}{2} when ± is plus. Add -18 to 2\sqrt{17}.

$$x=\frac{2\sqrt{17}-18}{2}$$

Divide -18+2\sqrt{17} by 2.

$$x=\sqrt{17}-9$$

Now solve the equation x=\frac{-18±2\sqrt{17}}{2} when ± is minus. Subtract 2\sqrt{17} from -18.

$$x=\frac{-2\sqrt{17}-18}{2}$$

Divide -18-2\sqrt{17} by 2.

$$x=-\sqrt{17}-9$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -9+\sqrt{17} for x_{1} and -9-\sqrt{17} for x_{2}.

$$x^{2}+18x+64=\left(x-\left(\sqrt{17}-9\right)\right)\left(x-\left(-\sqrt{17}-9\right)\right)$$

Evaluate

$$x^{2}+18x+64$$