Solve left(x+3right)^2=9

$${ \left(x+3 \right) }^{ 2 } =9$$

Solve for x

$$x=0$$

$$x=-6$$

Steps Using Factoring

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$x^{2}+6x+9=9$$

Subtract 9 from both sides.

$$x^{2}+6x+9-9=0$$

Subtract 9 from 9 to get 0.

$$x^{2}+6x=0$$

Factor out x.

$$x\left(x+6\right)=0$$

To find equation solutions, solve x=0 and x+6=0.

$$x=0 x=-6$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$x^{2}+6x+9=9$$

Subtract 9 from both sides.

$$x^{2}+6x+9-9=0$$

Subtract 9 from 9 to get 0.

$$x^{2}+6x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}}}{2}$$

Take the square root of 6^{2}.

$$x=\frac{-6±6}{2}$$

Now solve the equation x=\frac{-6±6}{2} when ± is plus. Add -6 to 6.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-6±6}{2} when ± is minus. Subtract 6 from -6.

$$x=-\frac{12}{2}$$

Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=0 x=-6$$

Steps for Completing the Square

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{9}$$

Simplify.

$$x+3=3 x+3=-3$$

Subtract 3 from both sides of the equation.

$$x=0 x=-6$$