Solve 3(x-2)^2=5?

$$3 ( x - 2 ) ^ { 2 } = 5 ?$$

Solve for x

$$x=\frac{\sqrt{15}}{3}+2\approx 3.290994449$$

$$x=-\frac{\sqrt{15}}{3}+2\approx 0.709005551$$

Steps by Finding Square Root

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Take the square root of both sides of the equation.

$$x-2=\frac{\sqrt{15}}{3} x-2=-\frac{\sqrt{15}}{3}$$

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\frac{\sqrt{15}}{3}-\left(-2\right) x-2-\left(-2\right)=-\frac{\sqrt{15}}{3}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\frac{\sqrt{15}}{3}-\left(-2\right) x=-\frac{\sqrt{15}}{3}-\left(-2\right)$$

Subtract -2 from \frac{\sqrt{15}}{3}.

$$x=\frac{\sqrt{15}}{3}+2$$

Subtract -2 from -\frac{\sqrt{15}}{3}.

$$x=-\frac{\sqrt{15}}{3}+2$$

The equation is now solved.

$$x=\frac{\sqrt{15}}{3}+2 x=-\frac{\sqrt{15}}{3}+2$$