Solve x^2+16x+32

$${ x }^{ 2 } +16x+32$$

Factor

$$\left(x-\left(-4\sqrt{2}-8\right)\right)\left(x-\left(4\sqrt{2}-8\right)\right)$$

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.

$$x^{2}+16x+32=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\times 32}}{2}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\times 32}}{2}$$

Multiply -4 times 32.

$$x=\frac{-16±\sqrt{256-128}}{2}$$

Add 256 to -128.

$$x=\frac{-16±\sqrt{128}}{2}$$

Take the square root of 128.

$$x=\frac{-16±8\sqrt{2}}{2}$$

Now solve the equation x=\frac{-16±8\sqrt{2}}{2} when ± is plus. Add -16 to 8\sqrt{2}.

$$x=\frac{8\sqrt{2}-16}{2}$$

Divide -16+8\sqrt{2} by 2.

$$x=4\sqrt{2}-8$$

Now solve the equation x=\frac{-16±8\sqrt{2}}{2} when ± is minus. Subtract 8\sqrt{2} from -16.

$$x=\frac{-8\sqrt{2}-16}{2}$$

Divide -16-8\sqrt{2} by 2.

$$x=-4\sqrt{2}-8$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -8+4\sqrt{2} for x_{1} and -8-4\sqrt{2} for x_{2}.

$$x^{2}+16x+32=\left(x-\left(4\sqrt{2}-8\right)\right)\left(x-\left(-4\sqrt{2}-8\right)\right)$$

Evaluate

$$x^{2}+16x+32$$