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Solve for x (complex solution)
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x^{2}+1=0
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.
x^{2}=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
x=i x=-i
The equation is now solved.
x^{2}+1=0
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.
x=\frac{0±\sqrt{0^{2}-4}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4}}{2}
Square 0.
x=\frac{0±2i}{2}
Take the square root of -4.
x=i
Now solve the equation x=\frac{0±2i}{2} when ± is plus.
x=-i
Now solve the equation x=\frac{0±2i}{2} when ± is minus.
x=i x=-i
The equation is now solved.