Solve (x-1)^2=224

$$( x - 1 ) ^ { 2 } = 224$$

Solve for x

$$x=4\sqrt{14}+1\approx 15.966629547$$

$$x=1-4\sqrt{14}\approx -13.966629547$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-1=4\sqrt{14} x-1=-4\sqrt{14}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=4\sqrt{14}-\left(-1\right) x-1-\left(-1\right)=-4\sqrt{14}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=4\sqrt{14}-\left(-1\right) x=-4\sqrt{14}-\left(-1\right)$$

Subtract -1 from 4\sqrt{14}.

$$x=4\sqrt{14}+1$$

Subtract -1 from -4\sqrt{14}.

$$x=1-4\sqrt{14}$$

The equation is now solved.

$$x=4\sqrt{14}+1 x=1-4\sqrt{14}$$