Solve (x+4)(x+4)=44

$$( x + 4 ) ( x + 4 ) = 44$$

Solve for x

$$x=2\sqrt{11}-4\approx 2.633249581$$

$$x=-2\sqrt{11}-4\approx -10.633249581$$

Steps Using the Quadratic Formula

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

$$\left(x+4\right)^{2}=44$$

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

$$x^{2}+8x+16=44$$

Subtract 44 from both sides.

$$x^{2}+8x+16-44=0$$

Subtract 44 from 16 to get -28.

$$x^{2}+8x-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-28\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-28\right)}}{2}$$

Multiply -4 times -28.

$$x=\frac{-8±\sqrt{64+112}}{2}$$

Add 64 to 112.

$$x=\frac{-8±\sqrt{176}}{2}$$

Take the square root of 176.

$$x=\frac{-8±4\sqrt{11}}{2}$$

Now solve the equation x=\frac{-8±4\sqrt{11}}{2} when ± is plus. Add -8 to 4\sqrt{11}.

$$x=\frac{4\sqrt{11}-8}{2}$$

Divide -8+4\sqrt{11} by 2.

$$x=2\sqrt{11}-4$$

Now solve the equation x=\frac{-8±4\sqrt{11}}{2} when ± is minus. Subtract 4\sqrt{11} from -8.

$$x=\frac{-4\sqrt{11}-8}{2}$$

Divide -8-4\sqrt{11} by 2.

$$x=-2\sqrt{11}-4$$

The equation is now solved.

$$x=2\sqrt{11}-4 x=-2\sqrt{11}-4$$

Steps for Completing the Square

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

$$\left(x+4\right)^{2}=44$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{44}$$

Simplify.

$$x+4=2\sqrt{11} x+4=-2\sqrt{11}$$

Subtract 4 from both sides of the equation.

$$x=2\sqrt{11}-4 x=-2\sqrt{11}-4$$