Solve (x-3)^2=6

$$( x - 3 ) ^ { 2 } = 6$$

Solve for x

$$x=\sqrt{6}+3\approx 5.449489743$$

$$x=3-\sqrt{6}\approx 0.550510257$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-3=\sqrt{6} x-3=-\sqrt{6}$$

Add 3 to both sides of the equation.

$$x-3-\left(-3\right)=\sqrt{6}-\left(-3\right) x-3-\left(-3\right)=-\sqrt{6}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$x=\sqrt{6}-\left(-3\right) x=-\sqrt{6}-\left(-3\right)$$

Subtract -3 from \sqrt{6}.

$$x=\sqrt{6}+3$$

Subtract -3 from -\sqrt{6}.

$$x=3-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6}+3 x=3-\sqrt{6}$$