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Solve for m
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m^{2}=-9
Subtract 9 from both sides. Anything subtracted from zero gives its negation.
m=3i m=-3i
The equation is now solved.
m^{2}+9=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
m=\frac{0±\sqrt{0^{2}-4\times 9}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
m=\frac{0±\sqrt{-4\times 9}}{2}
Square 0.
m=\frac{0±\sqrt{-36}}{2}
Multiply -4 times 9.
m=\frac{0±6i}{2}
Take the square root of -36.
m=3i
Now solve the equation m=\frac{0±6i}{2} when ± is plus.
m=-3i
Now solve the equation m=\frac{0±6i}{2} when ± is minus.
m=3i m=-3i
The equation is now solved.