Solve 1000(1+x)^2=1440

$$1000 ( 1 + x ) ^ { 2 } = 1440$$

Solve for x

$$x=\frac{1}{5}=0.2$$

$$x = -\frac{11}{5} = -2\frac{1}{5} = -2.2$$

Steps by Finding Square Root

Divide both sides by 1000.

$$\frac{1000\left(x+1\right)^{2}}{1000}=\frac{1440}{1000}$$

Dividing by 1000 undoes the multiplication by 1000.

$$\left(x+1\right)^{2}=\frac{1440}{1000}$$

Reduce the fraction \frac{1440}{1000} to lowest terms by extracting and canceling out 40.

$$\left(x+1\right)^{2}=\frac{36}{25}$$

Take the square root of both sides of the equation.

$$x+1=\frac{6}{5} x+1=-\frac{6}{5}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{6}{5}-1 x+1-1=-\frac{6}{5}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{6}{5}-1 x=-\frac{6}{5}-1$$

Subtract 1 from \frac{6}{5}.

$$x=\frac{1}{5}$$

Subtract 1 from -\frac{6}{5}.

$$x=-\frac{11}{5}$$

The equation is now solved.

$$x=\frac{1}{5} x=-\frac{11}{5}$$