Solve for y

Steps by Finding Square Root
Steps Using the Quadratic Formula
Solve for x (complex solution)


Solve for y (complex solution)

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y=\sqrt{x^{3}-4x} y=-\sqrt{x^{3}-4x}
Take the square root of both sides of the equation.
y^{2}-x^{3}=-4x
Subtract x^{3} from both sides.
y^{2}-x^{3}+4x=0
Add 4x to both sides.
y^{2}+4x-x^{3}=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.
y=\frac{0±\sqrt{0^{2}-4\left(4x-x^{3}\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 4x-x^{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
y=\frac{0±\sqrt{-4\left(4x-x^{3}\right)}}{2}
Square 0.
y=\frac{0±\sqrt{4x^{3}-16x}}{2}
Multiply -4 times 4x-x^{3}.
y=\frac{0±2\sqrt{x^{3}-4x}}{2}
Take the square root of -16x+4x^{3}.
y=\sqrt{x^{3}-4x}
Now solve the equation y=\frac{0±2\sqrt{x^{3}-4x}}{2} when ± is plus.
y=-\sqrt{x^{3}-4x}
Now solve the equation y=\frac{0±2\sqrt{x^{3}-4x}}{2} when ± is minus.
y=\sqrt{x^{3}-4x} y=-\sqrt{x^{3}-4x}
The equation is now solved.