Solve (x-5)^2=2

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

Solve for x

$$x=\sqrt{2}+5\approx 6.414213562$$

$$x=5-\sqrt{2}\approx 3.585786438$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-5=\sqrt{2} x-5=-\sqrt{2}$$

Add 5 to both sides of the equation.

$$x-5-\left(-5\right)=\sqrt{2}-\left(-5\right) x-5-\left(-5\right)=-\sqrt{2}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$x=\sqrt{2}-\left(-5\right) x=-\sqrt{2}-\left(-5\right)$$

Subtract -5 from \sqrt{2}.

$$x=\sqrt{2}+5$$

Subtract -5 from -\sqrt{2}.

$$x=5-\sqrt{2}$$

The equation is now solved.

$$x=\sqrt{2}+5 x=5-\sqrt{2}$$