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When you do this-- when you square this, you get 5x plus 6. So we get x is equal to 15, but we need to make sure that this actually works for our original equation. And this is the principal root of 81 so it's positive 9.

If you square the square root of 5x plus 6, you're going to get 5x plus 6. On the left-hand side, we have 5x and on the right-hand side, we have 75. We get x is equal to-- let's see, it's 15, right? Maybe this would have worked if this was the negative square root. So it's 3 plus 9 needs to be equal to 12, which is absolutely true.

Substitute 17 in for x, and we get √(17 - 1) = 4, or √(16) = 4.

For this problem, the number 17 works, so we have confirmed it as the answer.

Otherwise, I would lose the ability to say that they're equal. And now, we can square both sides of this equation.

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