Step by step
The question
Question: solve x² − 36 = 0.
x2 − 36 = 0
1 Get x² alone
There is no x term, so we get x² by itself.
To remove the − 36, we add 36 on both sides.
x2 − 36 + 36 = 0 + 36
0 + 36 = 36.
Now we have x² = 36.
x2 = 36
2 Square root of both sides
x squared is 36.
So x is the square root of 36, or minus it.
Minus times minus is plus, so the negative one works too.
x² = k → x = √k or x = −√k
6 × 6 = 36, (−6) × (−6) = 36
6 times 6 is 36.
So x = 6 or x = −6.
x = 6 or x = −6
Careful!
Many people write only x = 6.
They lose the minus answer.
Careful: not only x = 6 ✗
3 Check
Let's check: put x = 6 into the left side.
x = 6: 62 − 36 = 36 − 36 = 0
We get 0, the same as the right side.
It works!
Now put x = −6 into the left side.
x = −6: (−6)2 − 36 = 36 − 36 = 0
We get 0 again, the same as the right side.
So both answers are right!
Let's look back.
First: get x² alone.
Then: square root of both sides.
Last: check.
Answer
x = 6 or x = −6