Solve 4y^2=19

$$4 y ^ { 2 } = 19$$

Solve for y

$$y = \frac{\sqrt{19}}{2} \approx 2.179449472$$

$$y = -\frac{\sqrt{19}}{2} \approx -2.179449472$$

Steps by Finding Square Root

Divide both sides by 4.

$$y^{2}=\frac{19}{4}$$

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{19}}{2} y=-\frac{\sqrt{19}}{2}$$

Steps Using the Quadratic Formula

Divide both sides by 4.

$$y^{2}=\frac{19}{4}$$

Subtract \frac{19}{4} from both sides.

$$y^{2}-\frac{19}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{19}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{19}{4}\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{19}{4}\right)}}{2}$$

Multiply -4 times -\frac{19}{4}.

$$y=\frac{0±\sqrt{19}}{2}$$

Now solve the equation y=\frac{0±\sqrt{19}}{2} when ± is plus.

$$y=\frac{\sqrt{19}}{2}$$

Now solve the equation y=\frac{0±\sqrt{19}}{2} when ± is minus.

$$y=-\frac{\sqrt{19}}{2}$$

The equation is now solved.

$$y=\frac{\sqrt{19}}{2} y=-\frac{\sqrt{19}}{2}$$