Solve 1960=1/2(40)U^2+198

$$1960 = 1 / 2 ( 40 ) U ^ { 2 } + 198$$

Solve for U

$$U = \frac{\sqrt{8810}}{10} \approx 9.386160024$$

$$U = -\frac{\sqrt{8810}}{10} \approx -9.386160024$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 40 to get 20.

$$1960=20U^{2}+198$$

Swap sides so that all variable terms are on the left hand side.

$$20U^{2}+198=1960$$

Subtract 198 from both sides.

$$20U^{2}=1960-198$$

Subtract 198 from 1960 to get 1762.

$$20U^{2}=1762$$

Divide both sides by 20.

$$U^{2}=\frac{1762}{20}$$

Reduce the fraction \frac{1762}{20} to lowest terms by extracting and canceling out 2.

$$U^{2}=\frac{881}{10}$$

Take the square root of both sides of the equation.

$$U=\frac{\sqrt{8810}}{10} U=-\frac{\sqrt{8810}}{10}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 40 to get 20.

$$1960=20U^{2}+198$$

Swap sides so that all variable terms are on the left hand side.

$$20U^{2}+198=1960$$

Subtract 1960 from both sides.

$$20U^{2}+198-1960=0$$

Subtract 1960 from 198 to get -1762.

$$20U^{2}-1762=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -1762 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$U=\frac{0±\sqrt{0^{2}-4\times 20\left(-1762\right)}}{2\times 20}$$

Square 0.

$$U=\frac{0±\sqrt{-4\times 20\left(-1762\right)}}{2\times 20}$$

Multiply -4 times 20.

$$U=\frac{0±\sqrt{-80\left(-1762\right)}}{2\times 20}$$

Multiply -80 times -1762.

$$U=\frac{0±\sqrt{140960}}{2\times 20}$$

Take the square root of 140960.

$$U=\frac{0±4\sqrt{8810}}{2\times 20}$$

Multiply 2 times 20.

$$U=\frac{0±4\sqrt{8810}}{40}$$

Now solve the equation U=\frac{0±4\sqrt{8810}}{40} when ± is plus.

$$U=\frac{\sqrt{8810}}{10}$$

Now solve the equation U=\frac{0±4\sqrt{8810}}{40} when ± is minus.

$$U=-\frac{\sqrt{8810}}{10}$$

The equation is now solved.

$$U=\frac{\sqrt{8810}}{10} U=-\frac{\sqrt{8810}}{10}$$