Solve {l}{54=-10n}{text{Solvefor}otext{where}}{o=2n^2-2n}

$$\left. \begin{array} { l } { 54 = -10 n }\\ { \text{Solve for } o \text{ where} } \\ { o = 2 n ^ {2} - 2 n } \end{array} \right.$$

Solve for n, o

$$o = \frac{1728}{25} = 69\frac{3}{25} = 69.12$$

Solution Steps

Consider the first equation. Divide both sides by -10.

$$\frac{54}{-10}=n$$

Reduce the fraction \frac{54}{-10} to lowest terms by extracting and canceling out 2.

$$-\frac{27}{5}=n$$

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

$$n=-\frac{27}{5}$$

Consider the second equation. Insert the known values of variables into the equation.

$$o=2\left(-\frac{27}{5}\right)^{2}-2\left(-\frac{27}{5}\right)$$

Calculate -\frac{27}{5} to the power of 2 and get \frac{729}{25}.

$$o=2\times \frac{729}{25}-2\left(-\frac{27}{5}\right)$$

Multiply 2 and \frac{729}{25} to get \frac{1458}{25}.

$$o=\frac{1458}{25}-2\left(-\frac{27}{5}\right)$$

Multiply -2 and -\frac{27}{5} to get \frac{54}{5}.

$$o=\frac{1458}{25}+\frac{54}{5}$$

Add \frac{1458}{25} and \frac{54}{5} to get \frac{1728}{25}.

$$o=\frac{1728}{25}$$

The system is now solved.

$$n=-\frac{27}{5} o=\frac{1728}{25}$$