Create and solve one-variable equations and inequalities from contexts using all studied expression types, including simple root functions.
Write and solve a radical equation from a context
Problem
Solve \(\sqrt{x^2~+~9}~=~5\) and verify all solutions.
Big Picture
What this problem is really about
Because the radical is isolated and both sides are nonnegative, squaring is a valid way to expose the equation underneath. When that equation determines a square, remember that opposite inputs can produce the same squared value. Substitute every candidate into the original radical equation before retaining it.
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