Solve (x+7)(x+7)=49

$$(x+7)(x+7)=49$$

Solve for x

$$x=0$$

$$x=-14$$

Steps Using the Quadratic Formula

Multiply x+7 and x+7 to get \left(x+7\right)^{2}.

$$\left(x+7\right)^{2}=49$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+7\right)^{2}.

$$x^{2}+14x+49=49$$

Subtract 49 from both sides.

$$x^{2}+14x+49-49=0$$

Subtract 49 from 49 to get 0.

$$x^{2}+14x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 14 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}}}{2}$$

Take the square root of 14^{2}.

$$x=\frac{-14±14}{2}$$

Now solve the equation x=\frac{-14±14}{2} when ± is plus. Add -14 to 14.

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

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-14±14}{2} when ± is minus. Subtract 14 from -14.

$$x=-\frac{28}{2}$$

Divide -28 by 2.

$$x=-14$$

The equation is now solved.

$$x=0 x=-14$$

Steps for Completing the Square

Multiply x+7 and x+7 to get \left(x+7\right)^{2}.

$$\left(x+7\right)^{2}=49$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+7\right)^{2}}=\sqrt{49}$$

Simplify.

$$x+7=7 x+7=-7$$

Subtract 7 from both sides of the equation.

$$x=0 x=-14$$