Solve 22=1/2(87)v^2

$$22 = 1 / 2 ( 87 ) v ^ { 2 }$$

Solve for v

$$v=\frac{2\sqrt{957}}{87}\approx 0.711159002$$

$$v=-\frac{2\sqrt{957}}{87}\approx -0.711159002$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 87 to get \frac{87}{2}.

$$22=\frac{87}{2}v^{2}$$

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

$$\frac{87}{2}v^{2}=22$$

Multiply both sides by \frac{2}{87}, the reciprocal of \frac{87}{2}.

$$v^{2}=22\times \frac{2}{87}$$

Multiply 22 and \frac{2}{87} to get \frac{44}{87}.

$$v^{2}=\frac{44}{87}$$

Take the square root of both sides of the equation.

$$v=\frac{2\sqrt{957}}{87} v=-\frac{2\sqrt{957}}{87}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 87 to get \frac{87}{2}.

$$22=\frac{87}{2}v^{2}$$

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

$$\frac{87}{2}v^{2}=22$$

Subtract 22 from both sides.

$$\frac{87}{2}v^{2}-22=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{87}{2} for a, 0 for b, and -22 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times \frac{87}{2}\left(-22\right)}}{2\times \frac{87}{2}}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times \frac{87}{2}\left(-22\right)}}{2\times \frac{87}{2}}$$

Multiply -4 times \frac{87}{2}.

$$v=\frac{0±\sqrt{-174\left(-22\right)}}{2\times \frac{87}{2}}$$

Multiply -174 times -22.

$$v=\frac{0±\sqrt{3828}}{2\times \frac{87}{2}}$$

Take the square root of 3828.

$$v=\frac{0±2\sqrt{957}}{2\times \frac{87}{2}}$$

Multiply 2 times \frac{87}{2}.

$$v=\frac{0±2\sqrt{957}}{87}$$

Now solve the equation v=\frac{0±2\sqrt{957}}{87} when ± is plus.

$$v=\frac{2\sqrt{957}}{87}$$

Now solve the equation v=\frac{0±2\sqrt{957}}{87} when ± is minus.

$$v=-\frac{2\sqrt{957}}{87}$$

The equation is now solved.

$$v=\frac{2\sqrt{957}}{87} v=-\frac{2\sqrt{957}}{87}$$