Step by step
The question
Question: solve (x − 2)² = 9.
(x − 2)2 = 9
1 Square root of both sides
Something squared is 9.
So that something is the square root of 9, or minus it.
Both work, because minus times minus is plus.
( )² = k → ( ) = √k or −√k
The square root of 9 is 3, because 3 times 3 is 9.
x − 2 = 3 or x − 2 = −3
Careful!
Many people write only x − 2 = 3.
They lose the minus answer.
Careful: not only x − 2 = 3 ✗
2 Get x alone
To remove the − 2, we add 2 on both sides.
We do it in both equations.
x = 3 + 2 or x = −3 + 2
So x = 5 or x = −1.
x = 5 or x = −1
3 Check
Let's check: put x = 5 into the left side.
x = 5: 52 − 4(5) + 4 = 25 − 20 + 4 = 9
We get 9, the same as the right side.
It works!
Now put x = −1 into the left side.
x = −1: (−1)2 − 4(−1) + 4 = 1 + 4 + 4 = 9
We get 9 again, the same as the right side.
So both answers are right!
Let's look back.
First: square root of both sides.
Then: get x alone.
Last: check.
Answer
x = 5 or x = −1