Solve for x

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Solve for x (complex solution)

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