Step by step
The question
Question: solve √(x + 9) = 3.
√x + 9 = 3
1 Square both sides
Squaring removes the square root.
The square root of 9 is 3, and 3 squared is 9 again.
(√9)² = 9
We square both sides, so they stay equal.
(√x + 9)2 = 32
The square removes the square root.
3 squared is 9.
x + 9 = 9
2 Remove the + 9
We want x by itself.
The + 9 is in the way.
To remove + 9, we take away 9.
We do it on both sides, so they stay equal.
x + 9 − 9 = 9 − 9
+ 9 and − 9 make zero.
Cross them out.
9 − 9 = 0.
9 − 9 = 0
So x = 0!
x = 0
3 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.
Careful: squaring can make a false answer
(−2)² = 4 and 2² = 4
Let's check x = 0 in the question.
The left side is 3.
x = 0: √0 + 9 = √9 = 3
The right side is 3.
The same!
x = 0 works.
right side: 3 ✓
Let's look back.
First: square both sides.
Then: remove the + 9.
Last: check.
Answer
x = 0