Solve for x
x=13
x=-13
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x^{2}-169=0
Subtract 169 from both sides.
\left(x-13\right)\left(x+13\right)=0
Consider x^{2}-169. Rewrite x^{2}-169 as x^{2}-13^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=13 x=-13
To find equation solutions, solve x-13=0 and x+13=0.
x=13 x=-13
Take the square root of both sides of the equation.
x^{2}-169=0
Subtract 169 from both sides.
x=\frac{0±\sqrt{0^{2}-4\left(-169\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -169 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-169\right)}}{2}
Square 0.
x=\frac{0±\sqrt{676}}{2}
Multiply -4 times -169.
x=\frac{0±26}{2}
Take the square root of 676.
x=13
Now solve the equation x=\frac{0±26}{2} when ± is plus. Divide 26 by 2.
x=-13
Now solve the equation x=\frac{0±26}{2} when ± is minus. Divide -26 by 2.
x=13 x=-13
The equation is now solved.
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