Solve 3000=125*3^-1*k*2*k

$$3000 = 125 \times 3 ^ { - 1 } \times k \times 2 \times k$$

Solve for k

$$k=6$$

$$k=-6$$

Steps by Finding Square Root

Multiply k and k to get k^{2}.

$$3000=125\times 3^{-1}k^{2}\times 2$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$3000=125\times \frac{1}{3}k^{2}\times 2$$

Multiply 125 and \frac{1}{3} to get \frac{125}{3}.

$$3000=\frac{125}{3}k^{2}\times 2$$

Multiply \frac{125}{3} and 2 to get \frac{250}{3}.

$$3000=\frac{250}{3}k^{2}$$

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

$$\frac{250}{3}k^{2}=3000$$

Multiply both sides by \frac{3}{250}, the reciprocal of \frac{250}{3}.

$$k^{2}=3000\times \frac{3}{250}$$

Multiply 3000 and \frac{3}{250} to get 36.

$$k^{2}=36$$

Take the square root of both sides of the equation.

$$k=6 k=-6$$

Steps Using the Quadratic Formula

Multiply k and k to get k^{2}.

$$3000=125\times 3^{-1}k^{2}\times 2$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$3000=125\times \frac{1}{3}k^{2}\times 2$$

Multiply 125 and \frac{1}{3} to get \frac{125}{3}.

$$3000=\frac{125}{3}k^{2}\times 2$$

Multiply \frac{125}{3} and 2 to get \frac{250}{3}.

$$3000=\frac{250}{3}k^{2}$$

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

$$\frac{250}{3}k^{2}=3000$$

Subtract 3000 from both sides.

$$\frac{250}{3}k^{2}-3000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{250}{3} for a, 0 for b, and -3000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times \frac{250}{3}\left(-3000\right)}}{2\times \frac{250}{3}}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times \frac{250}{3}\left(-3000\right)}}{2\times \frac{250}{3}}$$

Multiply -4 times \frac{250}{3}.

$$k=\frac{0±\sqrt{-\frac{1000}{3}\left(-3000\right)}}{2\times \frac{250}{3}}$$

Multiply -\frac{1000}{3} times -3000.

$$k=\frac{0±\sqrt{1000000}}{2\times \frac{250}{3}}$$

Take the square root of 1000000.

$$k=\frac{0±1000}{2\times \frac{250}{3}}$$

Multiply 2 times \frac{250}{3}.

$$k=\frac{0±1000}{\frac{500}{3}}$$

Now solve the equation k=\frac{0±1000}{\frac{500}{3}} when ± is plus. Divide 1000 by \frac{500}{3} by multiplying 1000 by the reciprocal of \frac{500}{3}.

$$k=6$$

Now solve the equation k=\frac{0±1000}{\frac{500}{3}} when ± is minus. Divide -1000 by \frac{500}{3} by multiplying -1000 by the reciprocal of \frac{500}{3}.

$$k=-6$$

The equation is now solved.

$$k=6 k=-6$$