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x^{2}-49=0
Multiply both sides of the equation by 49.
\left(x-7\right)\left(x+7\right)=0
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).
x=7 x=-7
To find equation solutions, solve x-7=0 and x+7=0.
x^{2}-49=0
Multiply both sides of the equation by 49.
x^{2}=49
Add 49 to both sides. Anything plus zero gives itself.
x=7 x=-7
Take the square root of both sides of the equation.
x^{2}-49=0
Multiply both sides of the equation by 49.
x=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}
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{-4\left(-49\right)}}{2}
Square 0.
x=\frac{0±\sqrt{196}}{2}
Multiply -4 times -49.
x=\frac{0±14}{2}
Take the square root of 196.
x=7
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.
x=7 x=-7
The equation is now solved.