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In $3-38,$ solve each equation for the variable, check, and write the solution set.$$a-2=\sqrt{2 a-1}$$

$\{5\}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 8

Solving Radical Equations

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $3-38,$ solve each equa…

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All right. So we're gonna solve this equation here Checker Answer and then provide the solution set for a here. So I have the radical isolated, so I'm just gonna multiply both sides. I'm sorry. I'm gonna square both sides. So here, I've got a foil. So remember that when I have this thing squared, have got to do first so that a squared outer is the negative to a another negative to a So that's minus four A. And then a negative. Two times the negative two is four. So over on this side, I have a squared minus for a plus four. And this side square it is to a minus one. So I'm going to get everything over Thio the left side here. And so I'm left with a squared minus six. A plus five is equal to zero. So now I'm gonna factor this left side. And if I have a positive here in a negative here, that means this has gotta be two negatives here and then the factors of five are one and five. And so it doesn't matter the order here. And so let's check each one of these. Said it equal to zero because if this term is equal to 00 times, this would be a zero. And if this right side here is a zero, it will also turn this into a zero. So I get a minus. One is equal to zero, which means that a would be equal to one and then a minus five equals zero means that they would be equal to five. So now we're just gonna check both of these. So I checked both these in my original equation. So a minus two. So let's start with 11 minus two, equal to the square root of two plugging in one for a minus one. A one minus two is a negative 12 times one is two minus one is a square root of one. So when I take the square with the one that's the one and negative one is not equal to one. So this one here does not check out. Now let's put the five end. So if I have five minus two equal to the square root of two times five minus one, I get five. Minus two is three and then here five times two is 10 minus one is the square root of nine. The square root of nine is three. So this one here checks out. So my solution sat here is for when a is equal to five for this equation here.

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