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Solve for x (complex solution)
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25x^{2}=-36
Subtract 36 from both sides. Anything subtracted from zero gives its negation.
x^{2}=-\frac{36}{25}
Divide both sides by 25.
x=\frac{6}{5}i x=-\frac{6}{5}i
The equation is now solved.
25x^{2}+36=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 25\times 36}}{2\times 25}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 25\times 36}}{2\times 25}
Square 0.
x=\frac{0±\sqrt{-100\times 36}}{2\times 25}
Multiply -4 times 25.
x=\frac{0±\sqrt{-3600}}{2\times 25}
Multiply -100 times 36.
x=\frac{0±60i}{2\times 25}
Take the square root of -3600.
x=\frac{0±60i}{50}
Multiply 2 times 25.
x=\frac{6}{5}i
Now solve the equation x=\frac{0±60i}{50} when ± is plus.
x=-\frac{6}{5}i
Now solve the equation x=\frac{0±60i}{50} when ± is minus.
x=\frac{6}{5}i x=-\frac{6}{5}i
The equation is now solved.