Step by step
The question
Question: solve √(x + 2) = 1.
√x + 2 = 1
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 + 2)2 = 12
The square removes the square root.
1 squared is 1.
x + 2 = 1
2 Remove the + 2
We want x by itself.
The + 2 is in the way.
To remove + 2, we take away 2.
We do it on both sides, so they stay equal.
x + 2 − 2 = 1 − 2
+ 2 and − 2 make zero.
Cross them out.
1 − 2 = −1.
1 − 2 = −1
So x = −1!
x = −1
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 = −1 in the question.
The left side is 1.
x = −1: √−1 + 2 = √1 = 1
The right side is 1.
The same!
x = −1 works.
right side: 1 ✓
Let's look back.
First: square both sides.
Then: remove the + 2.
Last: check.
Answer
x = −1