Solve E-131.7=68.3:E=

$$E - 131.7 = 68.3 : E =$$

Solve for E

$$E = \frac{\sqrt{1761809} + 1317}{20} \approx 132.216576678$$

$$E=\frac{1317-\sqrt{1761809}}{20}\approx -0.516576678$$

Steps Using the Quadratic Formula

Variable E cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by E.

$$EE+E\left(-131.7\right)=68.3$$

Multiply E and E to get E^{2}.

$$E^{2}+E\left(-131.7\right)=68.3$$

Subtract 68.3 from both sides.

$$E^{2}+E\left(-131.7\right)-68.3=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$E^{2}-131.7E-68.3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -131.7 for b, and -68.3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$E=\frac{-\left(-131.7\right)±\sqrt{\left(-131.7\right)^{2}-4\left(-68.3\right)}}{2}$$

Square -131.7 by squaring both the numerator and the denominator of the fraction.

$$E=\frac{-\left(-131.7\right)±\sqrt{17344.89-4\left(-68.3\right)}}{2}$$

Multiply -4 times -68.3.

$$E=\frac{-\left(-131.7\right)±\sqrt{17344.89+273.2}}{2}$$

Add 17344.89 to 273.2 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$E=\frac{-\left(-131.7\right)±\sqrt{17618.09}}{2}$$

Take the square root of 17618.09.

$$E=\frac{-\left(-131.7\right)±\frac{\sqrt{1761809}}{10}}{2}$$

The opposite of -131.7 is 131.7.

$$E=\frac{131.7±\frac{\sqrt{1761809}}{10}}{2}$$

Now solve the equation E=\frac{131.7±\frac{\sqrt{1761809}}{10}}{2} when ± is plus. Add 131.7 to \frac{\sqrt{1761809}}{10}.

$$E=\frac{\sqrt{1761809}+1317}{2\times 10}$$

Divide \frac{1317+\sqrt{1761809}}{10} by 2.

$$E=\frac{\sqrt{1761809}+1317}{20}$$

Now solve the equation E=\frac{131.7±\frac{\sqrt{1761809}}{10}}{2} when ± is minus. Subtract \frac{\sqrt{1761809}}{10} from 131.7.

$$E=\frac{1317-\sqrt{1761809}}{2\times 10}$$

Divide \frac{1317-\sqrt{1761809}}{10} by 2.

$$E=\frac{1317-\sqrt{1761809}}{20}$$

The equation is now solved.

$$E=\frac{\sqrt{1761809}+1317}{20} E=\frac{1317-\sqrt{1761809}}{20}$$

Steps for Completing the Square

Variable E cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by E.

$$EE+E\left(-131.7\right)=68.3$$

Multiply E and E to get E^{2}.

$$E^{2}+E\left(-131.7\right)=68.3$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$E^{2}-131.7E=68.3$$

Divide -131.7, the coefficient of the x term, by 2 to get -65.85. Then add the square of -65.85 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$E^{2}-131.7E+\left(-65.85\right)^{2}=68.3+\left(-65.85\right)^{2}$$

Square -65.85 by squaring both the numerator and the denominator of the fraction.

$$E^{2}-131.7E+4336.2225=68.3+4336.2225$$

Add 68.3 to 4336.2225 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$E^{2}-131.7E+4336.2225=4404.5225$$

Factor E^{2}-131.7E+4336.2225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(E-65.85\right)^{2}=4404.5225$$

Take the square root of both sides of the equation.

$$\sqrt{\left(E-65.85\right)^{2}}=\sqrt{4404.5225}$$

Simplify.

$$E-65.85=\frac{\sqrt{1761809}}{20} E-65.85=-\frac{\sqrt{1761809}}{20}$$

Add 65.85 to both sides of the equation.

$$E=\frac{\sqrt{1761809}+1317}{20} E=\frac{1317-\sqrt{1761809}}{20}$$