Solve 7.5left(1+xright)^2=10.8

$$7.5 { \left( 1+x \right) }^{ 2 } =10.8$$

Solve for x

$$x=0.2$$

$$x=-2.2$$

Steps by Finding Square Root

Divide both sides of the equation by 7.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{7.5\left(x+1\right)^{2}}{7.5}=\frac{10.8}{7.5}$$

Dividing by 7.5 undoes the multiplication by 7.5.

$$\left(x+1\right)^{2}=\frac{10.8}{7.5}$$

Divide 10.8 by 7.5 by multiplying 10.8 by the reciprocal of 7.5.

$$\left(x+1\right)^{2}=1.44$$

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.

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