Solve (x+10)(x+10)=100

$$(x+10)(x+10)=100$$

Solve for x

$$x=0$$

$$x=-20$$

Steps Using the Quadratic Formula

Multiply x+10 and x+10 to get \left(x+10\right)^{2}.

$$\left(x+10\right)^{2}=100$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+10\right)^{2}.

$$x^{2}+20x+100=100$$

Subtract 100 from both sides.

$$x^{2}+20x+100-100=0$$

Subtract 100 from 100 to get 0.

$$x^{2}+20x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 20 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}}}{2}$$

Take the square root of 20^{2}.

$$x=\frac{-20±20}{2}$$

Now solve the equation x=\frac{-20±20}{2} when ± is plus. Add -20 to 20.

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

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-20±20}{2} when ± is minus. Subtract 20 from -20.

$$x=-\frac{40}{2}$$

Divide -40 by 2.

$$x=-20$$

The equation is now solved.

$$x=0 x=-20$$

Steps for Completing the Square

Multiply x+10 and x+10 to get \left(x+10\right)^{2}.

$$\left(x+10\right)^{2}=100$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{100}$$

Simplify.

$$x+10=10 x+10=-10$$

Subtract 10 from both sides of the equation.

$$x=0 x=-20$$