Solve y^2=-7

$${ y }^{ 2 } = -7$$

Solve for y

$$y=-\sqrt{7}i\approx -0-2.645751311i$$

$$y=\sqrt{7}i\approx 2.645751311i$$

Steps by Finding Square Root

The equation is now solved.

$$y=\sqrt{7}i y=-\sqrt{7}i$$

Steps Using the Quadratic Formula

Add 7 to both sides.

$$y^{2}+7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 7}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 7}}{2}$$

Multiply -4 times 7.

$$y=\frac{0±\sqrt{-28}}{2}$$

Take the square root of -28.

$$y=\frac{0±2\sqrt{7}i}{2}$$

Now solve the equation y=\frac{0±2\sqrt{7}i}{2} when ± is plus.

$$y=\sqrt{7}i$$

Now solve the equation y=\frac{0±2\sqrt{7}i}{2} when ± is minus.

$$y=-\sqrt{7}i$$

The equation is now solved.

$$y=\sqrt{7}i y=-\sqrt{7}i$$