c^2=(10^2+7^2)
You asked:
Solve the equation \({c}^{2} = {10}^{2} + {7}^{2}\) for the variable \(c\).
MathBot Answer:
\[\begin{aligned}c &= \sqrt{149} \approx 12.206556\\c &= - \sqrt{149} \approx -12.206556\end{aligned}\]
Take the square root of both sides of the equation $$\begin{aligned}c^{2} &= 7^{2} + 10^{2} \\ \sqrt{c^{2}} &= \sqrt{7^{2} + 10^{2}} \end{aligned}$$
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. $$\begin{aligned}c &= \pm \sqrt{7^{2} + 10^{2}} \\ c = \sqrt{7^{2} + 10^{2}} &,\, c=-\sqrt{7^{2} + 10^{2}}\end{aligned}$$