Solve (x-2)^2/8=9

$$\frac { ( x - 2 ) ^ { 2 } } { 8 } = 9$$

Solve for x

$$x=6\sqrt{2}+2\approx 10.485281374$$

$$x=2-6\sqrt{2}\approx -6.485281374$$

Steps by Finding Square Root

Multiply both sides by 8.

$$\frac{\frac{1}{8}\left(x-2\right)^{2}}{\frac{1}{8}}=\frac{9}{\frac{1}{8}}$$

Dividing by \frac{1}{8} undoes the multiplication by \frac{1}{8}.

$$\left(x-2\right)^{2}=\frac{9}{\frac{1}{8}}$$

Divide 9 by \frac{1}{8} by multiplying 9 by the reciprocal of \frac{1}{8}.

$$\left(x-2\right)^{2}=72$$

Take the square root of both sides of the equation.

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

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=6\sqrt{2}-\left(-2\right) x-2-\left(-2\right)=-6\sqrt{2}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=6\sqrt{2}-\left(-2\right) x=-6\sqrt{2}-\left(-2\right)$$

Subtract -2 from 6\sqrt{2}.

$$x=6\sqrt{2}+2$$

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

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

The equation is now solved.

$$x=6\sqrt{2}+2 x=2-6\sqrt{2}$$