c^2 = (25/16)-(1/81)
You asked:
Solve the equation \({c}^{2} = \frac{25}{16} - \frac{1}{81}\) for the variable \(c\).
MathBot Answer:
\[\begin{aligned}c &= \frac{7 \sqrt{41}}{36} \approx 1.2450519\\c &= - \frac{7 \sqrt{41}}{36} \approx -1.2450519\end{aligned}\]
Take the square root of both sides of the equation $$\begin{aligned}c^{2} &= - \frac{1}{81} + \frac{25}{16} \\ \sqrt{c^{2}} &= \sqrt{- \frac{1}{81} + \frac{25}{16}} \end{aligned}$$
Remember that both positive and negative numbers will result in a positive number when squared, so a square root will have both a positive and a negative answer. $$\begin{aligned}c &= \pm \sqrt{- \frac{1}{81} + \frac{25}{16}} \\ c = \sqrt{- \frac{1}{81} + \frac{25}{16}} &,\, c=-\sqrt{- \frac{1}{81} + \frac{25}{16}}\end{aligned}$$