Solve (x+8)(x+8)-2=0

$$(x+8)(x+8)-2=0$$

Solve for x

$$x=\sqrt{2}-8\approx -6.585786438$$

$$x=-\left(\sqrt{2}+8\right)\approx -9.414213562$$

Steps Using the Quadratic Formula

Multiply x+8 and x+8 to get \left(x+8\right)^{2}.

$$\left(x+8\right)^{2}-2=0$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+8\right)^{2}.

$$x^{2}+16x+64-2=0$$

Subtract 2 from 64 to get 62.

$$x^{2}+16x+62=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and 62 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\times 62}}{2}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\times 62}}{2}$$

Multiply -4 times 62.

$$x=\frac{-16±\sqrt{256-248}}{2}$$

Add 256 to -248.

$$x=\frac{-16±\sqrt{8}}{2}$$

Take the square root of 8.

$$x=\frac{-16±2\sqrt{2}}{2}$$

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

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

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

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

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

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

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

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

The equation is now solved.

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

Steps for Completing the Square

Multiply x+8 and x+8 to get \left(x+8\right)^{2}.

$$\left(x+8\right)^{2}-2=0$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+8\right)^{2}.

$$x^{2}+16x+64-2=0$$

Subtract 2 from 64 to get 62.

$$x^{2}+16x+62=0$$

Subtract 62 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}+16x=-62$$

Divide 16, the coefficient of the x term, by 2 to get 8. Then add the square of 8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+16x+8^{2}=-62+8^{2}$$

Square 8.

$$x^{2}+16x+64=-62+64$$

Add -62 to 64.

$$x^{2}+16x+64=2$$

Factor x^{2}+16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+8\right)^{2}=2$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{2}$$

Simplify.

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

Subtract 8 from both sides of the equation.

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