Solve 80(1+x)^2=1152

$$80 ( 1 + x ) ^ { 2 } = 1152$$

Solve for x

$$x=\frac{6\sqrt{10}}{5}-1\approx 2.794733192$$

$$x=-\frac{6\sqrt{10}}{5}-1\approx -4.794733192$$

Steps by Finding Square Root

Divide both sides by 80.

$$\frac{80\left(x+1\right)^{2}}{80}=\frac{1152}{80}$$

Dividing by 80 undoes the multiplication by 80.

$$\left(x+1\right)^{2}=\frac{1152}{80}$$

Reduce the fraction \frac{1152}{80} to lowest terms by extracting and canceling out 16.

$$\left(x+1\right)^{2}=\frac{72}{5}$$

Take the square root of both sides of the equation.

$$x+1=\frac{6\sqrt{10}}{5} x+1=-\frac{6\sqrt{10}}{5}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{6\sqrt{10}}{5}-1 x+1-1=-\frac{6\sqrt{10}}{5}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{6\sqrt{10}}{5}-1 x=-\frac{6\sqrt{10}}{5}-1$$