Solve 5(r-2)^2=35

$$5 ( r - 2 ) ^ { 2 } = 35$$

Solve for r

$$r=\sqrt{7}+2\approx 4.645751311$$

$$r=2-\sqrt{7}\approx -0.645751311$$

Steps by Finding Square Root

Divide both sides by 5.

$$\frac{5\left(r-2\right)^{2}}{5}=\frac{35}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\left(r-2\right)^{2}=\frac{35}{5}$$

Divide 35 by 5.

$$\left(r-2\right)^{2}=7$$

Take the square root of both sides of the equation.

$$r-2=\sqrt{7} r-2=-\sqrt{7}$$

Add 2 to both sides of the equation.

$$r-2-\left(-2\right)=\sqrt{7}-\left(-2\right) r-2-\left(-2\right)=-\sqrt{7}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$r=\sqrt{7}-\left(-2\right) r=-\sqrt{7}-\left(-2\right)$$

Subtract -2 from \sqrt{7}.

$$r=\sqrt{7}+2$$

Subtract -2 from -\sqrt{7}.

$$r=2-\sqrt{7}$$

The equation is now solved.

$$r=\sqrt{7}+2 r=2-\sqrt{7}$$