Solve 2500=1/310q^2

$$2500 = \frac { 1 } { 3 } 10 q ^ { 2 }$$

Solve for q

$$q=5\sqrt{30}\approx 27.386127875$$

$$q=-5\sqrt{30}\approx -27.386127875$$

Steps by Finding Square Root

Multiply \frac{1}{3} and 10 to get \frac{10}{3}.

$$2500=\frac{10}{3}q^{2}$$

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

$$\frac{10}{3}q^{2}=2500$$

Multiply both sides by \frac{3}{10}, the reciprocal of \frac{10}{3}.

$$q^{2}=2500\times \frac{3}{10}$$

Multiply 2500 and \frac{3}{10} to get 750.

$$q^{2}=750$$

Take the square root of both sides of the equation.

$$q=5\sqrt{30} q=-5\sqrt{30}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{3} and 10 to get \frac{10}{3}.

$$2500=\frac{10}{3}q^{2}$$

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

$$\frac{10}{3}q^{2}=2500$$

Subtract 2500 from both sides.

$$\frac{10}{3}q^{2}-2500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{10}{3} for a, 0 for b, and -2500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\times \frac{10}{3}\left(-2500\right)}}{2\times \frac{10}{3}}$$

Square 0.

$$q=\frac{0±\sqrt{-4\times \frac{10}{3}\left(-2500\right)}}{2\times \frac{10}{3}}$$

Multiply -4 times \frac{10}{3}.

$$q=\frac{0±\sqrt{-\frac{40}{3}\left(-2500\right)}}{2\times \frac{10}{3}}$$

Multiply -\frac{40}{3} times -2500.

$$q=\frac{0±\sqrt{\frac{100000}{3}}}{2\times \frac{10}{3}}$$

Take the square root of \frac{100000}{3}.

$$q=\frac{0±\frac{100\sqrt{30}}{3}}{2\times \frac{10}{3}}$$

Multiply 2 times \frac{10}{3}.

$$q=\frac{0±\frac{100\sqrt{30}}{3}}{\frac{20}{3}}$$

Now solve the equation q=\frac{0±\frac{100\sqrt{30}}{3}}{\frac{20}{3}} when ± is plus.

$$q=5\sqrt{30}$$

Now solve the equation q=\frac{0±\frac{100\sqrt{30}}{3}}{\frac{20}{3}} when ± is minus.

$$q=-5\sqrt{30}$$

The equation is now solved.

$$q=5\sqrt{30} q=-5\sqrt{30}$$