Solve alpha^2=10

$$\alpha ^ { 2 } = 10$$

Solve for α

$$\alpha =\sqrt{10}\approx 3.16227766$$

$$\alpha =-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$\alpha =\sqrt{10} \alpha =-\sqrt{10}$$

Steps Using the Quadratic Formula

Subtract 10 from both sides.

$$\alpha ^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\alpha =\frac{0±\sqrt{0^{2}-4\left(-10\right)}}{2}$$

Square 0.

$$\alpha =\frac{0±\sqrt{-4\left(-10\right)}}{2}$$

Multiply -4 times -10.

$$\alpha =\frac{0±\sqrt{40}}{2}$$

Take the square root of 40.

$$\alpha =\frac{0±2\sqrt{10}}{2}$$

Now solve the equation \alpha =\frac{0±2\sqrt{10}}{2} when ± is plus.

$$\alpha =\sqrt{10}$$

Now solve the equation \alpha =\frac{0±2\sqrt{10}}{2} when ± is minus.

$$\alpha =-\sqrt{10}$$

The equation is now solved.

$$\alpha =\sqrt{10} \alpha =-\sqrt{10}$$