Solve 10000*(1+k%)^2=22500

$$10000 \times ( 1 + k \% ) ^ { 2 } = 22500$$

Solve for k

$$k=50$$

$$k=-250$$

Steps by Finding Square Root

Divide both sides by 10000.

$$\frac{10000\left(\frac{1}{100}k+1\right)^{2}}{10000}=\frac{22500}{10000}$$

Dividing by 10000 undoes the multiplication by 10000.

$$\left(\frac{1}{100}k+1\right)^{2}=\frac{22500}{10000}$$

Reduce the fraction \frac{22500}{10000} to lowest terms by extracting and canceling out 2500.

$$\left(\frac{1}{100}k+1\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\frac{1}{100}k+1=\frac{3}{2} \frac{1}{100}k+1=-\frac{3}{2}$$

Subtract 1 from both sides of the equation.

$$\frac{1}{100}k+1-1=\frac{3}{2}-1 \frac{1}{100}k+1-1=-\frac{3}{2}-1$$

Subtracting 1 from itself leaves 0.

$$\frac{1}{100}k=\frac{3}{2}-1 \frac{1}{100}k=-\frac{3}{2}-1$$

Subtract 1 from \frac{3}{2}.

$$\frac{1}{100}k=\frac{1}{2}$$

Subtract 1 from -\frac{3}{2}.

$$\frac{1}{100}k=-\frac{5}{2}$$

Multiply both sides by 100.

$$\frac{\frac{1}{100}k}{\frac{1}{100}}=\frac{\frac{1}{2}}{\frac{1}{100}} \frac{\frac{1}{100}k}{\frac{1}{100}}=-\frac{\frac{5}{2}}{\frac{1}{100}}$$

Dividing by \frac{1}{100} undoes the multiplication by \frac{1}{100}.

$$k=\frac{\frac{1}{2}}{\frac{1}{100}} k=-\frac{\frac{5}{2}}{\frac{1}{100}}$$

Divide \frac{1}{2} by \frac{1}{100} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{100}.

$$k=50$$

Divide -\frac{5}{2} by \frac{1}{100} by multiplying -\frac{5}{2} by the reciprocal of \frac{1}{100}.

$$k=-250$$

The equation is now solved.

$$k=50 k=-250$$