Solve left(x+7right)^2-49=0

$${ \left(x+7 \right) }^{ 2 } -49=0$$

Solve for x

$$x=0$$

$$x=-14$$

Steps Using Factoring

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

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

Subtract 49 from 49 to get 0.

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

Factor out x.

$$x\left(x+14\right)=0$$

To find equation solutions, solve x=0 and x+14=0.

$$x=0 x=-14$$

Steps Using the Quadratic Formula

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

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

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

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

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

Subtract 49 from 49 to get 0.

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

Divide 14, the coefficient of the x term, by 2 to get 7. Then add the square of 7 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+14x+7^{2}=7^{2}$$

Square 7.

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

Factor x^{2}+14x+49. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\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.

$$x=0 x=-14$$