Solve 10*30=1/2v^2

$$10 \cdot 30 = 1 / 2 v ^ { 2 }$$

Solve for v

$$v=10\sqrt{6}\approx 24.494897428$$

$$v=-10\sqrt{6}\approx -24.494897428$$

Steps by Finding Square Root

Multiply 10 and 30 to get 300.

$$300=\frac{1}{2}v^{2}$$

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

$$\frac{1}{2}v^{2}=300$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$v^{2}=300\times 2$$

Multiply 300 and 2 to get 600.

$$v^{2}=600$$

Take the square root of both sides of the equation.

$$v=10\sqrt{6} v=-10\sqrt{6}$$

Steps Using the Quadratic Formula

Multiply 10 and 30 to get 300.

$$300=\frac{1}{2}v^{2}$$

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

$$\frac{1}{2}v^{2}=300$$

Subtract 300 from both sides.

$$\frac{1}{2}v^{2}-300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2} for a, 0 for b, and -300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-300\right)}}{2\times \frac{1}{2}}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-300\right)}}{2\times \frac{1}{2}}$$

Multiply -4 times \frac{1}{2}.

$$v=\frac{0±\sqrt{-2\left(-300\right)}}{2\times \frac{1}{2}}$$

Multiply -2 times -300.

$$v=\frac{0±\sqrt{600}}{2\times \frac{1}{2}}$$

Take the square root of 600.

$$v=\frac{0±10\sqrt{6}}{2\times \frac{1}{2}}$$

Multiply 2 times \frac{1}{2}.

$$v=\frac{0±10\sqrt{6}}{1}$$

Now solve the equation v=\frac{0±10\sqrt{6}}{1} when ± is plus.

$$v=10\sqrt{6}$$

Now solve the equation v=\frac{0±10\sqrt{6}}{1} when ± is minus.

$$v=-10\sqrt{6}$$

The equation is now solved.

$$v=10\sqrt{6} v=-10\sqrt{6}$$