Solve 5000(1+x)^2=18200

$$5000 ( 1 + x ) ^ { 2 } = 18200$$

Solve for x

$$x=\frac{\sqrt{91}}{5}-1\approx 0.907878403$$

$$x=-\frac{\sqrt{91}}{5}-1\approx -2.907878403$$

Steps by Finding Square Root

Divide both sides by 5000.

$$\frac{5000\left(x+1\right)^{2}}{5000}=\frac{18200}{5000}$$

Dividing by 5000 undoes the multiplication by 5000.

$$\left(x+1\right)^{2}=\frac{18200}{5000}$$

Reduce the fraction \frac{18200}{5000} to lowest terms by extracting and canceling out 200.

$$\left(x+1\right)^{2}=\frac{91}{25}$$

Take the square root of both sides of the equation.

$$x+1=\frac{\sqrt{91}}{5} x+1=-\frac{\sqrt{91}}{5}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{\sqrt{91}}{5}-1 x+1-1=-\frac{\sqrt{91}}{5}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{\sqrt{91}}{5}-1 x=-\frac{\sqrt{91}}{5}-1$$