Solve alpha^2=0.5/2.5

$$\alpha ^ { 2 } = \frac { 0.5 } { 2.5 }$$

Solve for α

$$\alpha =\frac{\sqrt{5}}{5}\approx 0.447213595$$

$$\alpha =-\frac{\sqrt{5}}{5}\approx -0.447213595$$

Steps by Finding Square Root

Expand \frac{0.5}{2.5} by multiplying both numerator and the denominator by 10.

$$\alpha ^{2}=\frac{5}{25}$$

Reduce the fraction \frac{5}{25} to lowest terms by extracting and canceling out 5.

$$\alpha ^{2}=\frac{1}{5}$$

Take the square root of both sides of the equation.

$$\alpha =\frac{\sqrt{5}}{5} \alpha =-\frac{\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Expand \frac{0.5}{2.5} by multiplying both numerator and the denominator by 10.

$$\alpha ^{2}=\frac{5}{25}$$

Reduce the fraction \frac{5}{25} to lowest terms by extracting and canceling out 5.

$$\alpha ^{2}=\frac{1}{5}$$

Subtract \frac{1}{5} from both sides.

$$\alpha ^{2}-\frac{1}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\alpha =\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{5}\right)}}{2}$$

Square 0.

$$\alpha =\frac{0±\sqrt{-4\left(-\frac{1}{5}\right)}}{2}$$

Multiply -4 times -\frac{1}{5}.

$$\alpha =\frac{0±\sqrt{\frac{4}{5}}}{2}$$

Take the square root of \frac{4}{5}.

$$\alpha =\frac{0±\frac{2\sqrt{5}}{5}}{2}$$

Now solve the equation \alpha =\frac{0±\frac{2\sqrt{5}}{5}}{2} when ± is plus.

$$\alpha =\frac{\sqrt{5}}{5}$$

Now solve the equation \alpha =\frac{0±\frac{2\sqrt{5}}{5}}{2} when ± is minus.

$$\alpha =-\frac{\sqrt{5}}{5}$$

The equation is now solved.

$$\alpha =\frac{\sqrt{5}}{5} \alpha =-\frac{\sqrt{5}}{5}$$