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Solve for x (complex solution)
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x^{2}=2-5
Subtract 5 from both sides.
x^{2}=-3
Subtract 5 from 2 to get -3.
x=\sqrt{3}i x=-\sqrt{3}i
The equation is now solved.
x^{2}+5-2=0
Subtract 2 from both sides.
x^{2}+3=0
Subtract 2 from 5 to get 3.
x=\frac{0±\sqrt{0^{2}-4\times 3}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 3}}{2}
Square 0.
x=\frac{0±\sqrt{-12}}{2}
Multiply -4 times 3.
x=\frac{0±2\sqrt{3}i}{2}
Take the square root of -12.
x=\sqrt{3}i
Now solve the equation x=\frac{0±2\sqrt{3}i}{2} when ± is plus.
x=-\sqrt{3}i
Now solve the equation x=\frac{0±2\sqrt{3}i}{2} when ± is minus.
x=\sqrt{3}i x=-\sqrt{3}i
The equation is now solved.