Step by step
The question
Question: solve √(5 − x) = 3.
1 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.
3 squared is 9.
2 Remove the 5
We want x by itself.
The 5 is in the way.
To remove 5, we take away 5.
We do it on both sides, so they stay equal.
5 and − 5 make zero.
Cross them out.
9 − 5 = 4.
Now we have −x = 4.
3 Remove the −1
−x means −1 times x.
We want just x.
To remove times −1, we divide by −1.
We do it on both sides, so they stay equal.
−1 divided by −1 is 1.
So just x is left.
4 divided by −1 is −4.
So x = −4!
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 = −4 in the question.
The left side is 3.
The right side is 3.
The same!
x = −4 works.
Let's look back.
First: square both sides.
Then: remove the 5.
Then: remove the −1.
Last: check.