Solve for x

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Solve for x (complex solution)

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-x^{2}+2=y
Swap sides so that all variable terms are on the left hand side.
-x^{2}=y-2
Subtract 2 from both sides.
\frac{-x^{2}}{-1}=\frac{y-2}{-1}
Divide both sides by -1.
x^{2}=\frac{y-2}{-1}
Dividing by -1 undoes the multiplication by -1.
x^{2}=2-y
Divide y-2 by -1.
x=\sqrt{2-y} x=-\sqrt{2-y}
Take the square root of both sides of the equation.
-x^{2}+2=y
Swap sides so that all variable terms are on the left hand side.
-x^{2}+2-y=0
Subtract y from both sides.
x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(2-y\right)}}{2\left(-1\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -y+2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-1\right)\left(2-y\right)}}{2\left(-1\right)}
Square 0.
x=\frac{0±\sqrt{4\left(2-y\right)}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{0±\sqrt{8-4y}}{2\left(-1\right)}
Multiply 4 times -y+2.
x=\frac{0±2\sqrt{2-y}}{2\left(-1\right)}
Take the square root of -4y+8.
x=\frac{0±2\sqrt{2-y}}{-2}
Multiply 2 times -1.
x=-\sqrt{2-y}
Now solve the equation x=\frac{0±2\sqrt{2-y}}{-2} when ± is plus.
x=\sqrt{2-y}
Now solve the equation x=\frac{0±2\sqrt{2-y}}{-2} when ± is minus.
x=-\sqrt{2-y} x=\sqrt{2-y}
The equation is now solved.