Solve 37.5=1/212v^2

$$37.5 = \frac{ 1 }{ 2 } 12 { v }^{ 2 }$$

Solve for v

$$v=2.5$$

$$v=-2.5$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 12 to get 6.

$$37.5=6v^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$6v^{2}=37.5$$

Divide both sides by 6.

$$v^{2}=\frac{37.5}{6}$$

Expand \frac{37.5}{6} by multiplying both numerator and the denominator by 10.

$$v^{2}=\frac{375}{60}$$

Reduce the fraction \frac{375}{60} to lowest terms by extracting and canceling out 15.

$$v^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$v=\frac{5}{2} v=-\frac{5}{2}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 12 to get 6.

$$37.5=6v^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$6v^{2}=37.5$$

Subtract 37.5 from both sides.

$$6v^{2}-37.5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -37.5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times 6\left(-37.5\right)}}{2\times 6}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times 6\left(-37.5\right)}}{2\times 6}$$

Multiply -4 times 6.

$$v=\frac{0±\sqrt{-24\left(-37.5\right)}}{2\times 6}$$

Multiply -24 times -37.5.

$$v=\frac{0±\sqrt{900}}{2\times 6}$$

Take the square root of 900.

$$v=\frac{0±30}{2\times 6}$$

Multiply 2 times 6.

$$v=\frac{0±30}{12}$$

Now solve the equation v=\frac{0±30}{12} when ± is plus. Reduce the fraction \frac{30}{12} to lowest terms by extracting and canceling out 6.

$$v=\frac{5}{2}$$

Now solve the equation v=\frac{0±30}{12} when ± is minus. Reduce the fraction \frac{-30}{12} to lowest terms by extracting and canceling out 6.

$$v=-\frac{5}{2}$$

The equation is now solved.

$$v=\frac{5}{2} v=-\frac{5}{2}$$