Solve left(x-1right)^2=4/3

$${ \left(x-1 \right) }^{ 2 } = \frac{ 4 }{ 3 }$$

Solve for x

$$x=\frac{2\sqrt{3}}{3}+1\approx 2.154700538$$

$$x=-\frac{2\sqrt{3}}{3}+1\approx -0.154700538$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\frac{2\sqrt{3}}{3}-\left(-1\right) x-1-\left(-1\right)=-\frac{2\sqrt{3}}{3}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\frac{2\sqrt{3}}{3}-\left(-1\right) x=-\frac{2\sqrt{3}}{3}-\left(-1\right)$$

Subtract -1 from \frac{2\sqrt{3}}{3}.

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

Subtract -1 from -\frac{2\sqrt{3}}{3}.

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

The equation is now solved.

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