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x^{2}-2=0
Add -5 and 3 to get -2.
x^{2}=2
Add 2 to both sides. Anything plus zero gives itself.
x=\sqrt{2} x=-\sqrt{2}
Take the square root of both sides of the equation.
x^{2}-2=0
Add -5 and 3 to get -2.
x=\frac{0±\sqrt{0^{2}-4\left(-2\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-2\right)}}{2}
Square 0.
x=\frac{0±\sqrt{8}}{2}
Multiply -4 times -2.
x=\frac{0±2\sqrt{2}}{2}
Take the square root of 8.
x=\sqrt{2}
Now solve the equation x=\frac{0±2\sqrt{2}}{2} when ± is plus.
x=-\sqrt{2}
Now solve the equation x=\frac{0±2\sqrt{2}}{2} when ± is minus.
x=\sqrt{2} x=-\sqrt{2}
The equation is now solved.