Step by step
The question
Question: solve x² = 144.
x2 = 144
1 Square root of both sides
x squared is 144.
So x is the square root of 144, or minus it.
Minus times minus is plus, so the negative one works too.
x² = k → x = √k or x = −√k
12 × 12 = 144, (−12) × (−12) = 144
12 times 12 is 144.
So x = 12 or x = −12.
x = 12 or x = −12
Careful!
Many people write only x = 12.
They lose the minus answer.
Careful: not only x = 12 ✗
2 Check
Let's check: put x = 12 into the left side.
x = 12: 122 = 144
We get 144, the same as the right side.
It works!
Now put x = −12 into the left side.
x = −12: (−12)2 = 144
We get 144 again, the same as the right side.
So both answers are right!
Let's look back.
First: square root of both sides.
Last: check.
Answer
x = 12 or x = −12