Step by step
The question
Question: solve x² = 81.
x2 = 81
1 Square root of both sides
x squared is 81.
So x is the square root of 81, or minus it.
Minus times minus is plus, so the negative one works too.
x² = k → x = √k or x = −√k
9 × 9 = 81, (−9) × (−9) = 81
9 times 9 is 81.
So x = 9 or x = −9.
x = 9 or x = −9
Careful!
Many people write only x = 9.
They lose the minus answer.
Careful: not only x = 9 ✗
2 Check
Let's check: put x = 9 into the left side.
x = 9: 92 = 81
We get 81, the same as the right side.
It works!
Now put x = −9 into the left side.
x = −9: (−9)2 = 81
We get 81 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 = 9 or x = −9