Step by step
The question
Question: solve 2x² − 8 = 0.
2x2 − 8 = 0
1 Get x² alone
There is no x term, so we get x² by itself.
To remove the − 8, we add 8 on both sides.
2x2 − 8 + 8 = 0 + 8
0 + 8 = 8.
Now we have 2x² = 8.
2x2 = 8
To remove times 2, we divide both sides by 2.
2x22 = 82
8 divided by 2 is 4.
x2 = 4
2 Square root of both sides
x squared is 4.
So x is the square root of 4, or minus it.
Minus times minus is plus, so the negative one works too.
x² = k → x = √k or x = −√k
2 × 2 = 4, (−2) × (−2) = 4
2 times 2 is 4.
So x = 2 or x = −2.
x = 2 or x = −2
Careful!
Many people write only x = 2.
They lose the minus answer.
Careful: not only x = 2 ✗
3 Check
Let's check: put x = 2 into the left side.
x = 2: 2(2)2 − 8 = 8 − 8 = 0
We get 0, the same as the right side.
It works!
Now put x = −2 into the left side.
x = −2: 2(−2)2 − 8 = 8 − 8 = 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 = 2 or x = −2