Solve (x-5)^2=42

$$( x - 5 ) ^ { 2 } = 42$$

Solve for x

$$x=\sqrt{42}+5\approx 11.480740698$$

$$x=5-\sqrt{42}\approx -1.480740698$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-5=\sqrt{42} x-5=-\sqrt{42}$$

Add 5 to both sides of the equation.

$$x-5-\left(-5\right)=\sqrt{42}-\left(-5\right) x-5-\left(-5\right)=-\sqrt{42}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$x=\sqrt{42}-\left(-5\right) x=-\sqrt{42}-\left(-5\right)$$

Subtract -5 from \sqrt{42}.

$$x=\sqrt{42}+5$$

Subtract -5 from -\sqrt{42}.

$$x=5-\sqrt{42}$$

The equation is now solved.

$$x=\sqrt{42}+5 x=5-\sqrt{42}$$