Solve psi^2=7

$$\psi ^ { 2 } = 7$$

Solve for ψ

$$\psi =\sqrt{7}\approx 2.645751311$$

$$\psi =-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$\psi =\sqrt{7} \psi =-\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$\psi ^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\psi =\frac{0±\sqrt{0^{2}-4\left(-7\right)}}{2}$$

Square 0.

$$\psi =\frac{0±\sqrt{-4\left(-7\right)}}{2}$$

Multiply -4 times -7.

$$\psi =\frac{0±\sqrt{28}}{2}$$

Take the square root of 28.

$$\psi =\frac{0±2\sqrt{7}}{2}$$

Now solve the equation \psi =\frac{0±2\sqrt{7}}{2} when ± is plus.

$$\psi =\sqrt{7}$$

Now solve the equation \psi =\frac{0±2\sqrt{7}}{2} when ± is minus.

$$\psi =-\sqrt{7}$$

The equation is now solved.

$$\psi =\sqrt{7} \psi =-\sqrt{7}$$