Skip to main content
Solve for x (complex solution)
Tick mark Image
Graph

Similar Problems from Web Search

Share

3x^{2}=-30
Subtract 30 from both sides. Anything subtracted from zero gives its negation.
x^{2}=\frac{-30}{3}
Divide both sides by 3.
x^{2}=-10
Divide -30 by 3 to get -10.
x=\sqrt{10}i x=-\sqrt{10}i
The equation is now solved.
3x^{2}+30=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 3\times 30}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 3\times 30}}{2\times 3}
Square 0.
x=\frac{0±\sqrt{-12\times 30}}{2\times 3}
Multiply -4 times 3.
x=\frac{0±\sqrt{-360}}{2\times 3}
Multiply -12 times 30.
x=\frac{0±6\sqrt{10}i}{2\times 3}
Take the square root of -360.
x=\frac{0±6\sqrt{10}i}{6}
Multiply 2 times 3.
x=\sqrt{10}i
Now solve the equation x=\frac{0±6\sqrt{10}i}{6} when ± is plus.
x=-\sqrt{10}i
Now solve the equation x=\frac{0±6\sqrt{10}i}{6} when ± is minus.
x=\sqrt{10}i x=-\sqrt{10}i
The equation is now solved.