Solve 112(1+x)^2=288

$$112 ( 1 + x ) ^ { 2 } = 288$$

Solve for x

$$x=\frac{3\sqrt{14}}{7}-1\approx 0.603567451$$

$$x=-\frac{3\sqrt{14}}{7}-1\approx -2.603567451$$

Steps by Finding Square Root

Divide both sides by 112.

$$\frac{112\left(x+1\right)^{2}}{112}=\frac{288}{112}$$

Dividing by 112 undoes the multiplication by 112.

$$\left(x+1\right)^{2}=\frac{288}{112}$$

Reduce the fraction \frac{288}{112} to lowest terms by extracting and canceling out 16.

$$\left(x+1\right)^{2}=\frac{18}{7}$$

Take the square root of both sides of the equation.

$$x+1=\frac{3\sqrt{14}}{7} x+1=-\frac{3\sqrt{14}}{7}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{3\sqrt{14}}{7}-1 x+1-1=-\frac{3\sqrt{14}}{7}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{3\sqrt{14}}{7}-1 x=-\frac{3\sqrt{14}}{7}-1$$