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Solve for x (complex solution)
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x^{2}=-\frac{9}{2}
Divide both sides by -2.
x=\frac{3\sqrt{2}i}{2} x=-\frac{3\sqrt{2}i}{2}
The equation is now solved.
x^{2}=-\frac{9}{2}
Divide both sides by -2.
x^{2}+\frac{9}{2}=0
Add \frac{9}{2} to both sides.
x=\frac{0±\sqrt{0^{2}-4\times \frac{9}{2}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{9}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times \frac{9}{2}}}{2}
Square 0.
x=\frac{0±\sqrt{-18}}{2}
Multiply -4 times \frac{9}{2}.
x=\frac{0±3\sqrt{2}i}{2}
Take the square root of -18.
x=\frac{3\sqrt{2}i}{2}
Now solve the equation x=\frac{0±3\sqrt{2}i}{2} when ± is plus.
x=-\frac{3\sqrt{2}i}{2}
Now solve the equation x=\frac{0±3\sqrt{2}i}{2} when ± is minus.
x=\frac{3\sqrt{2}i}{2} x=-\frac{3\sqrt{2}i}{2}
The equation is now solved.