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-x^{2}+6=2
Combine x^{2} and -2x^{2} to get -x^{2}.
-x^{2}=2-6
Subtract 6 from both sides.
-x^{2}=-4
Subtract 6 from 2 to get -4.
x^{2}=\frac{-4}{-1}
Divide both sides by -1.
x^{2}=4
Fraction \frac{-4}{-1} can be simplified to 4 by removing the negative sign from both the numerator and the denominator.
x=2 x=-2
Take the square root of both sides of the equation.
-x^{2}+6=2
Combine x^{2} and -2x^{2} to get -x^{2}.
-x^{2}+6-2=0
Subtract 2 from both sides.
-x^{2}+4=0
Subtract 2 from 6 to get 4.
x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 4}}{2\left(-1\right)}
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(-1\right)\times 4}}{2\left(-1\right)}
Square 0.
x=\frac{0±\sqrt{4\times 4}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{0±\sqrt{16}}{2\left(-1\right)}
Multiply 4 times 4.
x=\frac{0±4}{2\left(-1\right)}
Take the square root of 16.
x=\frac{0±4}{-2}
Multiply 2 times -1.
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.