Solve -2v^2=-148

$$- 2 v ^ { 2 } = - 148$$

Solve for v

$$v=\sqrt{74}\approx 8.602325267$$

$$v=-\sqrt{74}\approx -8.602325267$$

Steps by Finding Square Root

Divide both sides by -2.

$$v^{2}=\frac{-148}{-2}$$

Divide -148 by -2 to get 74.

$$v^{2}=74$$

Take the square root of both sides of the equation.

$$v=\sqrt{74} v=-\sqrt{74}$$

Steps Using the Quadratic Formula

Divide both sides by -2.

$$v^{2}=\frac{-148}{-2}$$

Divide -148 by -2 to get 74.

$$v^{2}=74$$

Subtract 74 from both sides.

$$v^{2}-74=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -74 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-74\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-74\right)}}{2}$$

Multiply -4 times -74.

$$v=\frac{0±\sqrt{296}}{2}$$

Take the square root of 296.

$$v=\frac{0±2\sqrt{74}}{2}$$

Now solve the equation v=\frac{0±2\sqrt{74}}{2} when ± is plus.

$$v=\sqrt{74}$$

Now solve the equation v=\frac{0±2\sqrt{74}}{2} when ± is minus.

$$v=-\sqrt{74}$$

The equation is now solved.

$$v=\sqrt{74} v=-\sqrt{74}$$