$a^{2}$ =12 $^{2}$ + -10 $^{2}$
You asked:
Solve the equation \({a}^{2} = {12}^{2} + -{10}^{2}\) for the variable \(a\).
MathBot Answer:
\[\begin{aligned}a &= 2 \sqrt{11} \approx 6.6332496\\a &= - 2 \sqrt{11} \approx -6.6332496\end{aligned}\]
Take the square root of both sides of the equation $$\begin{aligned}a^{2} &= - 10^{2} + 12^{2} \\ \sqrt{a^{2}} &= \sqrt{- 10^{2} + 12^{2}} \end{aligned}$$
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. $$\begin{aligned}a &= \pm \sqrt{- 10^{2} + 12^{2}} \\ a = \sqrt{- 10^{2} + 12^{2}} &,\, a=-\sqrt{- 10^{2} + 12^{2}}\end{aligned}$$