Solve (x+4)(x+4)=80

$$( x + 4 ) ( x + 4 ) = 80$$

Solve for x

$$x=4\sqrt{5}-4\approx 4.94427191$$

$$x=-4\sqrt{5}-4\approx -12.94427191$$

Steps Using the Quadratic Formula

Multiply x+4 and x+4 to get \left(x+4\right)^{2}.

$$\left(x+4\right)^{2}=80$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}+8x+16=80$$

Subtract 80 from both sides.

$$x^{2}+8x+16-80=0$$

Subtract 80 from 16 to get -64.

$$x^{2}+8x-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-64\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$x=\frac{-8±\sqrt{64+256}}{2}$$

Add 64 to 256.

$$x=\frac{-8±\sqrt{320}}{2}$$

Take the square root of 320.

$$x=\frac{-8±8\sqrt{5}}{2}$$

Now solve the equation x=\frac{-8±8\sqrt{5}}{2} when ± is plus. Add -8 to 8\sqrt{5}.

$$x=\frac{8\sqrt{5}-8}{2}$$

Divide -8+8\sqrt{5} by 2.

$$x=4\sqrt{5}-4$$

Now solve the equation x=\frac{-8±8\sqrt{5}}{2} when ± is minus. Subtract 8\sqrt{5} from -8.

$$x=\frac{-8\sqrt{5}-8}{2}$$

Divide -8-8\sqrt{5} by 2.

$$x=-4\sqrt{5}-4$$

The equation is now solved.

$$x=4\sqrt{5}-4 x=-4\sqrt{5}-4$$

Steps for Completing the Square

Multiply x+4 and x+4 to get \left(x+4\right)^{2}.

$$\left(x+4\right)^{2}=80$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{80}$$

Simplify.

$$x+4=4\sqrt{5} x+4=-4\sqrt{5}$$

Subtract 4 from both sides of the equation.

$$x=4\sqrt{5}-4 x=-4\sqrt{5}-4$$