Solve 5(w-1)^2=4

$$5 ( w - 1 ) ^ { 2 } = 4$$

Solve for w

$$w=\frac{2\sqrt{5}}{5}+1\approx 1.894427191$$

$$w=-\frac{2\sqrt{5}}{5}+1\approx 0.105572809$$

Steps by Finding Square Root

Divide both sides by 5.

$$\frac{5\left(w-1\right)^{2}}{5}=\frac{4}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\left(w-1\right)^{2}=\frac{4}{5}$$

Take the square root of both sides of the equation.

$$w-1=\frac{2\sqrt{5}}{5} w-1=-\frac{2\sqrt{5}}{5}$$

Add 1 to both sides of the equation.

$$w-1-\left(-1\right)=\frac{2\sqrt{5}}{5}-\left(-1\right) w-1-\left(-1\right)=-\frac{2\sqrt{5}}{5}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$w=\frac{2\sqrt{5}}{5}-\left(-1\right) w=-\frac{2\sqrt{5}}{5}-\left(-1\right)$$

Subtract -1 from \frac{2\sqrt{5}}{5}.

$$w=\frac{2\sqrt{5}}{5}+1$$

Subtract -1 from -\frac{2\sqrt{5}}{5}.

$$w=-\frac{2\sqrt{5}}{5}+1$$

The equation is now solved.

$$w=\frac{2\sqrt{5}}{5}+1 w=-\frac{2\sqrt{5}}{5}+1$$