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Solve for x (complex solution)
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4x^{2}+34=0
Add -35 and 69 to get 34.
4x^{2}=-34
Subtract 34 from both sides. Anything subtracted from zero gives its negation.
x^{2}=\frac{-34}{4}
Divide both sides by 4.
x^{2}=-\frac{17}{2}
Reduce the fraction \frac{-34}{4} to lowest terms by extracting and canceling out 2.
x=\frac{\sqrt{34}i}{2} x=-\frac{\sqrt{34}i}{2}
The equation is now solved.
4x^{2}+34=0
Add -35 and 69 to get 34.
x=\frac{0±\sqrt{0^{2}-4\times 4\times 34}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 34 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 4\times 34}}{2\times 4}
Square 0.
x=\frac{0±\sqrt{-16\times 34}}{2\times 4}
Multiply -4 times 4.
x=\frac{0±\sqrt{-544}}{2\times 4}
Multiply -16 times 34.
x=\frac{0±4\sqrt{34}i}{2\times 4}
Take the square root of -544.
x=\frac{0±4\sqrt{34}i}{8}
Multiply 2 times 4.
x=\frac{\sqrt{34}i}{2}
Now solve the equation x=\frac{0±4\sqrt{34}i}{8} when ± is plus.
x=-\frac{\sqrt{34}i}{2}
Now solve the equation x=\frac{0±4\sqrt{34}i}{8} when ± is minus.
x=\frac{\sqrt{34}i}{2} x=-\frac{\sqrt{34}i}{2}
The equation is now solved.