Solve 200(1+x%)^2=224.72

$$200 ( 1 + x \% ) ^ { 2 } = 224.72$$

Solve for x

$$x=6$$

$$x=-206$$

Steps by Finding Square Root

Divide both sides by 200.

$$\frac{200\left(\frac{1}{100}x+1\right)^{2}}{200}=\frac{224.72}{200}$$

Dividing by 200 undoes the multiplication by 200.

$$\left(\frac{1}{100}x+1\right)^{2}=\frac{224.72}{200}$$

Divide 224.72 by 200.

$$\left(\frac{1}{100}x+1\right)^{2}=1.1236$$

Take the square root of both sides of the equation.

$$\frac{1}{100}x+1=\frac{53}{50} \frac{1}{100}x+1=-\frac{53}{50}$$

Subtract 1 from both sides of the equation.

$$\frac{1}{100}x+1-1=\frac{53}{50}-1 \frac{1}{100}x+1-1=-\frac{53}{50}-1$$

Subtracting 1 from itself leaves 0.

$$\frac{1}{100}x=\frac{53}{50}-1 \frac{1}{100}x=-\frac{53}{50}-1$$

Subtract 1 from \frac{53}{50}.

$$\frac{1}{100}x=\frac{3}{50}$$

Subtract 1 from -\frac{53}{50}.

$$\frac{1}{100}x=-\frac{103}{50}$$

Multiply both sides by 100.

$$\frac{\frac{1}{100}x}{\frac{1}{100}}=\frac{\frac{3}{50}}{\frac{1}{100}} \frac{\frac{1}{100}x}{\frac{1}{100}}=-\frac{\frac{103}{50}}{\frac{1}{100}}$$

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

$$x=\frac{\frac{3}{50}}{\frac{1}{100}} x=-\frac{\frac{103}{50}}{\frac{1}{100}}$$

Divide \frac{3}{50} by \frac{1}{100} by multiplying \frac{3}{50} by the reciprocal of \frac{1}{100}.

$$x=6$$

Divide -\frac{103}{50} by \frac{1}{100} by multiplying -\frac{103}{50} by the reciprocal of \frac{1}{100}.

$$x=-206$$

The equation is now solved.

$$x=6 x=-206$$