Solve for x (complex solution)
x=-6\sqrt{2}i\approx -0-8.485281374i
x=6\sqrt{2}i\approx 8.485281374i
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x^{2}=-72
Subtract 72 from both sides. Anything subtracted from zero gives its negation.
x=6\sqrt{2}i x=-6\sqrt{2}i
The equation is now solved.
x^{2}+72=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.
x=\frac{0±\sqrt{0^{2}-4\times 72}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 72}}{2}
Square 0.
x=\frac{0±\sqrt{-288}}{2}
Multiply -4 times 72.
x=\frac{0±12\sqrt{2}i}{2}
Take the square root of -288.
x=6\sqrt{2}i
Now solve the equation x=\frac{0±12\sqrt{2}i}{2} when ± is plus.
x=-6\sqrt{2}i
Now solve the equation x=\frac{0±12\sqrt{2}i}{2} when ± is minus.
x=6\sqrt{2}i x=-6\sqrt{2}i
The equation is now solved.
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