Solve for x (complex solution)
x=-\frac{5\sqrt{3}i}{2}\approx -0-4.330127019i
x=\frac{5\sqrt{3}i}{2}\approx 4.330127019i
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4x^{2}=-75
Subtract 75 from both sides. Anything subtracted from zero gives its negation.
x^{2}=-\frac{75}{4}
Divide both sides by 4.
x=\frac{5\sqrt{3}i}{2} x=-\frac{5\sqrt{3}i}{2}
The equation is now solved.
4x^{2}+75=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 4\times 75}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 4\times 75}}{2\times 4}
Square 0.
x=\frac{0±\sqrt{-16\times 75}}{2\times 4}
Multiply -4 times 4.
x=\frac{0±\sqrt{-1200}}{2\times 4}
Multiply -16 times 75.
x=\frac{0±20\sqrt{3}i}{2\times 4}
Take the square root of -1200.
x=\frac{0±20\sqrt{3}i}{8}
Multiply 2 times 4.
x=\frac{5\sqrt{3}i}{2}
Now solve the equation x=\frac{0±20\sqrt{3}i}{8} when ± is plus.
x=-\frac{5\sqrt{3}i}{2}
Now solve the equation x=\frac{0±20\sqrt{3}i}{8} when ± is minus.
x=\frac{5\sqrt{3}i}{2} x=-\frac{5\sqrt{3}i}{2}
The equation is now solved.
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