Solve (w-1)^2-75=0,v

$$( w - 1 ) ^ { 2 } - 75 = 0 , v$$

Solve for w

$$w=5\sqrt{3}+1\approx 9.660254038$$

$$w=1-5\sqrt{3}\approx -7.660254038$$

Steps by Finding Square Root

Add 75 to both sides of the equation.

$$\left(w-1\right)^{2}-75+75=75$$

Subtracting 75 from itself leaves 0.

$$\left(w-1\right)^{2}=75$$

Take the square root of both sides of the equation.

$$w-1=5\sqrt{3} w-1=-5\sqrt{3}$$

Add 1 to both sides of the equation.

$$w-1-\left(-1\right)=5\sqrt{3}-\left(-1\right) w-1-\left(-1\right)=-5\sqrt{3}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$w=5\sqrt{3}-\left(-1\right) w=-5\sqrt{3}-\left(-1\right)$$

Subtract -1 from 5\sqrt{3}.

$$w=5\sqrt{3}+1$$

Subtract -1 from -5\sqrt{3}.

$$w=1-5\sqrt{3}$$

The equation is now solved.

$$w=5\sqrt{3}+1 w=1-5\sqrt{3}$$