Solve 4.5left(1+xright)^2=9

$$4.5 { \left(1+x \right) }^{ 2 } =9$$

Solve for x

$$x=\sqrt{2}-1\approx 0.414213562$$

$$x=-\left(\sqrt{2}+1\right)\approx -2.414213562$$

Steps by Finding Square Root

Divide both sides of the equation by 4.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{4.5\left(x+1\right)^{2}}{4.5}=\frac{9}{4.5}$$

Dividing by 4.5 undoes the multiplication by 4.5.

$$\left(x+1\right)^{2}=\frac{9}{4.5}$$

Divide 9 by 4.5 by multiplying 9 by the reciprocal of 4.5.

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

Take the square root of both sides of the equation.

$$x+1=\sqrt{2} x+1=-\sqrt{2}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\sqrt{2}-1 x+1-1=-\sqrt{2}-1$$

Subtracting 1 from itself leaves 0.

$$x=\sqrt{2}-1 x=-\sqrt{2}-1$$