Radical Equation Simplification

We have: $\sqrt{5x + 9} + \sqrt{5x - 9} = 6 + 3\sqrt{2} = \sqrt{36} + \sqrt{18}$ By inspection, matching terms: $\sqrt{5x + 9} = \sqrt{36} \implies 5x + 9 = 36 \implies 5x = 27$ Check second term: $\sqrt{5x - 9} = \sqrt{27 - 9} = \sqrt{18} = 3\sqrt{2}$, which matches.

Now, calculate $\sqrt{10x + 9}$: $\sqrt{10x + 9} = \sqrt{2(5x) + 9} = \sqrt{2(27) + 9} = \sqrt{63} = 3\sqrt{7}$