Step by step
The question
Question: solve √(x + 6) − 2 = 3.
1 Get the root alone
We want the square root by itself.
The − 2 is in the way.
To remove − 2, we add 2.
We do it on both sides, so they stay equal.
− 2 and + 2 make zero.
Cross them out.
3 plus 2 is 5.
Now we have √(x + 6) = 5.
2 Square both sides
Squaring removes the square root.
The square root of 9 is 3, and 3 squared is 9 again.
We square both sides, so they stay equal.
The square removes the square root.
5 squared is 25.
3 Remove the + 6
We want x by itself.
The + 6 is in the way.
To remove + 6, we take away 6.
We do it on both sides, so they stay equal.
+ 6 and − 6 make zero.
Cross them out.
25 − 6 = 19.
So x = 19!
4 Check
Careful!
Squaring can make an answer that does not work.
Why?
Minus 2 squared is 4, and 2 squared is 4 too.
Squaring hides a minus sign.
So we check every answer in the question.
Let's check x = 19 in the question.
The left side is 3.
The right side is 3.
The same!
x = 19 works.
Let's look back.
First: get the root alone.
Then: square both sides.
Then: remove the + 6.
Last: check.