Solve 2y^2+2=0

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

Solve for y

$$y=-i$$

$$y=i$$

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by 2.

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

Divide -2 by 2 to get -1.

$$y^{2}=-1$$

The equation is now solved.

$$y=i y=-i$$

Steps Using the Quadratic Formula

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.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$y=\frac{0±\sqrt{-8\times 2}}{2\times 2}$$

Multiply -8 times 2.

$$y=\frac{0±\sqrt{-16}}{2\times 2}$$

Take the square root of -16.

$$y=\frac{0±4i}{2\times 2}$$

Multiply 2 times 2.

$$y=\frac{0±4i}{4}$$

Now solve the equation y=\frac{0±4i}{4} when ± is plus.

$$y=i$$

Now solve the equation y=\frac{0±4i}{4} when ± is minus.

$$y=-i$$

The equation is now solved.

$$y=i y=-i$$