Solve (x-3)^2-50=0

$$( x - 3 ) ^ { 2 } - 50 = 0$$

Solve for x

$$x=5\sqrt{2}+3\approx 10.071067812$$

$$x=3-5\sqrt{2}\approx -4.071067812$$

Steps by Finding Square Root

Add 50 to both sides of the equation.

$$\left(x-3\right)^{2}-50+50=50$$

Subtracting 50 from itself leaves 0.

$$\left(x-3\right)^{2}=50$$

Take the square root of both sides of the equation.

$$x-3=5\sqrt{2} x-3=-5\sqrt{2}$$

Add 3 to both sides of the equation.

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

Subtracting -3 from itself leaves 0.

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

Subtract -3 from 5\sqrt{2}.

$$x=5\sqrt{2}+3$$

Subtract -3 from -5\sqrt{2}.

$$x=3-5\sqrt{2}$$

The equation is now solved.

$$x=5\sqrt{2}+3 x=3-5\sqrt{2}$$