Solve U^2-80+15=0

$$U ^ { 2 } - 80 + 15 = 0$$

Solve for U

$$U=\sqrt{65}\approx 8.062257748$$

$$U=-\sqrt{65}\approx -8.062257748$$

Steps by Finding Square Root

Add -80 and 15 to get -65.

$$U^{2}-65=0$$

Add 65 to both sides. Anything plus zero gives itself.

$$U^{2}=65$$

Take the square root of both sides of the equation.

$$U=\sqrt{65} U=-\sqrt{65}$$

Steps Using the Quadratic Formula

Add -80 and 15 to get -65.

$$U^{2}-65=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -65 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$U=\frac{0±\sqrt{0^{2}-4\left(-65\right)}}{2}$$

Square 0.

$$U=\frac{0±\sqrt{-4\left(-65\right)}}{2}$$

Multiply -4 times -65.

$$U=\frac{0±\sqrt{260}}{2}$$

Take the square root of 260.

$$U=\frac{0±2\sqrt{65}}{2}$$

Now solve the equation U=\frac{0±2\sqrt{65}}{2} when ± is plus.

$$U=\sqrt{65}$$

Now solve the equation U=\frac{0±2\sqrt{65}}{2} when ± is minus.

$$U=-\sqrt{65}$$

The equation is now solved.

$$U=\sqrt{65} U=-\sqrt{65}$$