Question

Solve the equation. $$16+x^{2}=64$$

Short answer

The solutions to the equation are \(x = 6.93\) and \(x = -6.93\).

Step-by-step solution

Isolate the quadratic term

First, isolate the \(x^{2}\) term by subtracting 16 from both sides of the equation. That gives \(x^{2}= 64 - 16 = 48\)

Determine the square root

Next, find the square root of 48. The square root of 48 yields two potential solutions, as we can have a positive root and a negative root. Hence, the solution for \(x^{2}=48\) are \(x = \sqrt{48}\) and \(x = -\sqrt{48}\). Given that \(\sqrt{48} \approx 6.93\), the values for x are \(x = 6.93\) and \(x = -6.93\).

Check the solutions if necessary

Given that the question does not require checking the solution, this step is not necessary for this particular exercise. However, in general, it is always a good idea to substitute the computed values back into the original equation to verify if they're correct.