Solve (x-1)^2/30=5/8

$$\frac { ( x - 1 ) ^ { 2 } } { 30 } = \frac { 5 } { 8 }$$

Solve for x

$$x=\frac{5\sqrt{3}}{2}+1\approx 5.330127019$$

$$x=-\frac{5\sqrt{3}}{2}+1\approx -3.330127019$$

Steps by Finding Square Root

Multiply both sides by 30.

$$\frac{\frac{1}{30}\left(x-1\right)^{2}}{\frac{1}{30}}=\frac{\frac{5}{8}}{\frac{1}{30}}$$

Dividing by \frac{1}{30} undoes the multiplication by \frac{1}{30}.

$$\left(x-1\right)^{2}=\frac{\frac{5}{8}}{\frac{1}{30}}$$

Divide \frac{5}{8} by \frac{1}{30} by multiplying \frac{5}{8} by the reciprocal of \frac{1}{30}.

$$\left(x-1\right)^{2}=\frac{75}{4}$$

Take the square root of both sides of the equation.

$$x-1=\frac{5\sqrt{3}}{2} x-1=-\frac{5\sqrt{3}}{2}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\frac{5\sqrt{3}}{2}-\left(-1\right) x-1-\left(-1\right)=-\frac{5\sqrt{3}}{2}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\frac{5\sqrt{3}}{2}-\left(-1\right) x=-\frac{5\sqrt{3}}{2}-\left(-1\right)$$

Subtract -1 from \frac{5\sqrt{3}}{2}.

$$x=\frac{5\sqrt{3}}{2}+1$$

Subtract -1 from -\frac{5\sqrt{3}}{2}.

$$x=-\frac{5\sqrt{3}}{2}+1$$

The equation is now solved.

$$x=\frac{5\sqrt{3}}{2}+1 x=-\frac{5\sqrt{3}}{2}+1$$