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x^{2}-4=0
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{3}.
\left(x-2\right)\left(x+2\right)=0
Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=2 x=-2
To find equation solutions, solve x-2=0 and x+2=0.
x^{2}-4=0
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{3}.
x^{2}=4
Add 4 to both sides. Anything plus zero gives itself.
x=2 x=-2
Take the square root of both sides of the equation.
x^{2}-4=0
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{3}.
x=\frac{0±\sqrt{0^{2}-4\left(-4\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-4\right)}}{2}
Square 0.
x=\frac{0±\sqrt{16}}{2}
Multiply -4 times -4.
x=\frac{0±4}{2}
Take the square root of 16.
x=2
Now solve the equation x=\frac{0±4}{2} when ± is plus. Divide 4 by 2.
x=-2
Now solve the equation x=\frac{0±4}{2} when ± is minus. Divide -4 by 2.
x=2 x=-2
The equation is now solved.