Solve 1/2V^2=10*60*60

$$\frac { 1 } { 2 } V ^ { 2 } = 10 \times 60 \times 60$$

Solve for V

$$V=120\sqrt{5}\approx 268.3281573$$

$$V=-120\sqrt{5}\approx -268.3281573$$

Steps by Finding Square Root

Multiply 10 and 60 to get 600.

$$\frac{1}{2}V^{2}=600\times 60$$

Multiply 600 and 60 to get 36000.

$$\frac{1}{2}V^{2}=36000$$

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

$$V^{2}=36000\times 2$$

Multiply 36000 and 2 to get 72000.

$$V^{2}=72000$$

Take the square root of both sides of the equation.

$$V=120\sqrt{5} V=-120\sqrt{5}$$

Steps Using the Quadratic Formula

Multiply 10 and 60 to get 600.

$$\frac{1}{2}V^{2}=600\times 60$$

Multiply 600 and 60 to get 36000.

$$\frac{1}{2}V^{2}=36000$$

Subtract 36000 from both sides.

$$\frac{1}{2}V^{2}-36000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2} for a, 0 for b, and -36000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$V=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-36000\right)}}{2\times \frac{1}{2}}$$

Square 0.

$$V=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-36000\right)}}{2\times \frac{1}{2}}$$

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

$$V=\frac{0±\sqrt{-2\left(-36000\right)}}{2\times \frac{1}{2}}$$

Multiply -2 times -36000.

$$V=\frac{0±\sqrt{72000}}{2\times \frac{1}{2}}$$

Take the square root of 72000.

$$V=\frac{0±120\sqrt{5}}{2\times \frac{1}{2}}$$

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

$$V=\frac{0±120\sqrt{5}}{1}$$

Now solve the equation V=\frac{0±120\sqrt{5}}{1} when ± is plus.

$$V=120\sqrt{5}$$

Now solve the equation V=\frac{0±120\sqrt{5}}{1} when ± is minus.

$$V=-120\sqrt{5}$$

The equation is now solved.

$$V=120\sqrt{5} V=-120\sqrt{5}$$