Solve 3(q-2)^2=21

$$3 ( q - 2 ) ^ { 2 } = 21$$

Solve for q

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

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

Steps by Finding Square Root

Divide both sides by 3.

$$\frac{3\left(q-2\right)^{2}}{3}=\frac{21}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(q-2\right)^{2}=\frac{21}{3}$$

Divide 21 by 3.

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

Take the square root of both sides of the equation.

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

Add 2 to both sides of the equation.

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

Subtracting -2 from itself leaves 0.

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

Subtract -2 from \sqrt{7}.

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

Subtract -2 from -\sqrt{7}.

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

The equation is now solved.

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