Solve (x/3+1)^2=3/2

$$( \frac { x } { 3 } + 1 ) ^ { 2 } = \frac { 3 } { 2 }$$

Solve for x

$$x=\frac{3\sqrt{6}}{2}-3\approx 0.674234614$$

$$x=-\frac{3\sqrt{6}}{2}-3\approx -6.674234614$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$\frac{1}{3}x+1=\frac{\sqrt{6}}{2} \frac{1}{3}x+1=-\frac{\sqrt{6}}{2}$$

Subtract 1 from both sides of the equation.

$$\frac{1}{3}x+1-1=\frac{\sqrt{6}}{2}-1 \frac{1}{3}x+1-1=-\frac{\sqrt{6}}{2}-1$$

Subtracting 1 from itself leaves 0.

$$\frac{1}{3}x=\frac{\sqrt{6}}{2}-1 \frac{1}{3}x=-\frac{\sqrt{6}}{2}-1$$

Subtract 1 from \frac{\sqrt{6}}{2}.

$$\frac{1}{3}x=\frac{\sqrt{6}}{2}-1$$

Subtract 1 from -\frac{\sqrt{6}}{2}.

$$\frac{1}{3}x=-\frac{\sqrt{6}}{2}-1$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}x}{\frac{1}{3}}=\frac{\frac{\sqrt{6}}{2}-1}{\frac{1}{3}} \frac{\frac{1}{3}x}{\frac{1}{3}}=\frac{-\frac{\sqrt{6}}{2}-1}{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$x=\frac{\frac{\sqrt{6}}{2}-1}{\frac{1}{3}} x=\frac{-\frac{\sqrt{6}}{2}-1}{\frac{1}{3}}$$

Divide \frac{\sqrt{6}}{2}-1 by \frac{1}{3} by multiplying \frac{\sqrt{6}}{2}-1 by the reciprocal of \frac{1}{3}.

$$x=\frac{3\sqrt{6}}{2}-3$$

Divide -\frac{\sqrt{6}}{2}-1 by \frac{1}{3} by multiplying -\frac{\sqrt{6}}{2}-1 by the reciprocal of \frac{1}{3}.

$$x=-\frac{3\sqrt{6}}{2}-3$$

The equation is now solved.

$$x=\frac{3\sqrt{6}}{2}-3 x=-\frac{3\sqrt{6}}{2}-3$$