Solve 1500left(1+xright)^2=18150

$$1500 { \left(1+x \right) }^{ 2 } =18150$$

Solve for x

$$x=\frac{11\sqrt{10}}{10}-1\approx 2.478505426$$

$$x=-\frac{11\sqrt{10}}{10}-1\approx -4.478505426$$

Steps by Finding Square Root

Divide both sides by 1500.

$$\frac{1500\left(x+1\right)^{2}}{1500}=\frac{18150}{1500}$$

Dividing by 1500 undoes the multiplication by 1500.

$$\left(x+1\right)^{2}=\frac{18150}{1500}$$

Reduce the fraction \frac{18150}{1500} to lowest terms by extracting and canceling out 150.

$$\left(x+1\right)^{2}=\frac{121}{10}$$

Take the square root of both sides of the equation.

$$x+1=\frac{11\sqrt{10}}{10} x+1=-\frac{11\sqrt{10}}{10}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{11\sqrt{10}}{10}-1 x+1-1=-\frac{11\sqrt{10}}{10}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{11\sqrt{10}}{10}-1 x=-\frac{11\sqrt{10}}{10}-1$$