Solve (x+2)*(x+2)=21

$$( x + 2 ) \cdot ( x + 2 ) = 21$$

Solve for x

$$x=\sqrt{21}-2\approx 2.582575695$$

$$x=-\left(\sqrt{21}+2\right)\approx -6.582575695$$

Steps Using the Quadratic Formula

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

$$\left(x+2\right)^{2}=21$$

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

$$x^{2}+4x+4=21$$

Subtract 21 from both sides.

$$x^{2}+4x+4-21=0$$

Subtract 21 from 4 to get -17.

$$x^{2}+4x-17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-17\right)}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-17\right)}}{2}$$

Multiply -4 times -17.

$$x=\frac{-4±\sqrt{16+68}}{2}$$

Add 16 to 68.

$$x=\frac{-4±\sqrt{84}}{2}$$

Take the square root of 84.

$$x=\frac{-4±2\sqrt{21}}{2}$$

Now solve the equation x=\frac{-4±2\sqrt{21}}{2} when ± is plus. Add -4 to 2\sqrt{21}.

$$x=\frac{2\sqrt{21}-4}{2}$$

Divide -4+2\sqrt{21} by 2.

$$x=\sqrt{21}-2$$

Now solve the equation x=\frac{-4±2\sqrt{21}}{2} when ± is minus. Subtract 2\sqrt{21} from -4.

$$x=\frac{-2\sqrt{21}-4}{2}$$

Divide -4-2\sqrt{21} by 2.

$$x=-\sqrt{21}-2$$

The equation is now solved.

$$x=\sqrt{21}-2 x=-\sqrt{21}-2$$

Steps for Completing the Square

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

$$\left(x+2\right)^{2}=21$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{21}$$

Simplify.

$$x+2=\sqrt{21} x+2=-\sqrt{21}$$

Subtract 2 from both sides of the equation.

$$x=\sqrt{21}-2 x=-\sqrt{21}-2$$