Solve y^2=-11/2

$$y ^ { 2 } = - \frac { 11 } { 2 }$$

Solve for y

$$y=-\frac{\sqrt{22}i}{2}\approx -0-2.34520788i$$

$$y=\frac{\sqrt{22}i}{2}\approx 2.34520788i$$

Steps by Finding Square Root

The equation is now solved.

$$y=\frac{\sqrt{22}i}{2} y=-\frac{\sqrt{22}i}{2}$$

Steps Using the Quadratic Formula

Add \frac{11}{2} to both sides.

$$y^{2}+\frac{11}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{11}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times \frac{11}{2}}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times \frac{11}{2}}}{2}$$

Multiply -4 times \frac{11}{2}.

$$y=\frac{0±\sqrt{-22}}{2}$$

Take the square root of -22.

$$y=\frac{0±\sqrt{22}i}{2}$$

Now solve the equation y=\frac{0±\sqrt{22}i}{2} when ± is plus.

$$y=\frac{\sqrt{22}i}{2}$$

Now solve the equation y=\frac{0±\sqrt{22}i}{2} when ± is minus.

$$y=-\frac{\sqrt{22}i}{2}$$

The equation is now solved.

$$y=\frac{\sqrt{22}i}{2} y=-\frac{\sqrt{22}i}{2}$$