Solve (a+1)^2=1

$$( a + 1 ) ^ { 2 } = 1$$

Solve for a

$$a=0$$

$$a=-2$$

Steps Using Factoring

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(a+1\right)^{2}.

$$a^{2}+2a+1=1$$

Subtract 1 from both sides.

$$a^{2}+2a+1-1=0$$

Subtract 1 from 1 to get 0.

$$a^{2}+2a=0$$

Factor out a.

$$a\left(a+2\right)=0$$

To find equation solutions, solve a=0 and a+2=0.

$$a=0 a=-2$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(a+1\right)^{2}.

$$a^{2}+2a+1=1$$

Subtract 1 from both sides.

$$a^{2}+2a+1-1=0$$

Subtract 1 from 1 to get 0.

$$a^{2}+2a=0$$

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

$$a=\frac{-2±\sqrt{2^{2}}}{2}$$

Take the square root of 2^{2}.

$$a=\frac{-2±2}{2}$$

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

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

Divide 0 by 2.

$$a=0$$

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

$$a=-\frac{4}{2}$$

Divide -4 by 2.

$$a=-2$$

The equation is now solved.

$$a=0 a=-2$$

Steps for Completing the Square

Take the square root of both sides of the equation.

$$\sqrt{\left(a+1\right)^{2}}=\sqrt{1}$$

Simplify.

$$a+1=1 a+1=-1$$

Subtract 1 from both sides of the equation.

$$a=0 a=-2$$