Consider $x^{2}-49$. Rewrite $x^{2}-49$ as $x^{2}-7^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-7\right)\left(x+7\right)=0$$
To find equation solutions, solve $x-7=0$ and $x+7=0$.
$$x=7$$ $$x=-7$$
Steps by Finding Square Root
Divide both sides by $7$.
$$x^{2}=\frac{343}{7}$$
Divide $343$ by $7$ to get $49$.
$$x^{2}=49$$
Take the square root of both sides of the equation.
$$x=7$$ $$x=-7$$
Steps Using the Quadratic Formula
Divide both sides by $7$.
$$x^{2}=\frac{343}{7}$$
Divide $343$ by $7$ to get $49$.
$$x^{2}=49$$
Subtract $49$ from both sides.
$$x^{2}-49=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-49$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}$$
Square $0$.
$$x=\frac{0±\sqrt{-4\left(-49\right)}}{2}$$
Multiply $-4$ times $-49$.
$$x=\frac{0±\sqrt{196}}{2}$$
Take the square root of $196$.
$$x=\frac{0±14}{2}$$
Now solve the equation $x=\frac{0±14}{2}$ when $±$ is plus. Divide $14$ by $2$.
$$x=7$$
Now solve the equation $x=\frac{0±14}{2}$ when $±$ is minus. Divide $-14$ by $2$.
