Solve 2y^2=4

$$2 y ^ { 2 } = 4$$

Solve for y

$$y=\sqrt{2}\approx 1.414213562$$

$$y=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Divide both sides by 2.

$$y^{2}=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$y^{2}=2$$

Take the square root of both sides of the equation.

$$y=\sqrt{2} y=-\sqrt{2}$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$y^{2}=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$y^{2}=2$$

Subtract 2 from both sides.

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

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

$$y=\frac{0±\sqrt{0^{2}-4\left(-2\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-2\right)}}{2}$$

Multiply -4 times -2.

$$y=\frac{0±\sqrt{8}}{2}$$

Take the square root of 8.

$$y=\frac{0±2\sqrt{2}}{2}$$

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

$$y=\sqrt{2}$$

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

$$y=-\sqrt{2}$$

The equation is now solved.

$$y=\sqrt{2} y=-\sqrt{2}$$