Solve (c+12)^2=144

$$( c + 12 ) ^ { 2 } = 144$$

Solve for c

$$c=0$$

$$c=-24$$

Steps Using Factoring

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(c+12\right)^{2}.

$$c^{2}+24c+144=144$$

Subtract 144 from both sides.

$$c^{2}+24c+144-144=0$$

Subtract 144 from 144 to get 0.

$$c^{2}+24c=0$$

Factor out c.

$$c\left(c+24\right)=0$$

To find equation solutions, solve c=0 and c+24=0.

$$c=0 c=-24$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(c+12\right)^{2}.

$$c^{2}+24c+144=144$$

Subtract 144 from both sides.

$$c^{2}+24c+144-144=0$$

Subtract 144 from 144 to get 0.

$$c^{2}+24c=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 24 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{-24±\sqrt{24^{2}}}{2}$$

Take the square root of 24^{2}.

$$c=\frac{-24±24}{2}$$

Now solve the equation c=\frac{-24±24}{2} when ± is plus. Add -24 to 24.

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

Divide 0 by 2.

$$c=0$$

Now solve the equation c=\frac{-24±24}{2} when ± is minus. Subtract 24 from -24.

$$c=-\frac{48}{2}$$

Divide -48 by 2.

$$c=-24$$

The equation is now solved.

$$c=0 c=-24$$

Steps for Completing the Square

Take the square root of both sides of the equation.

$$\sqrt{\left(c+12\right)^{2}}=\sqrt{144}$$

Simplify.

$$c+12=12 c+12=-12$$

Subtract 12 from both sides of the equation.

$$c=0 c=-24$$