Step by step
The question
Question: choose a method and solve 2x² = 32.
2x2 = 32
1 Choose the method
There is no x term.
So we can get x² alone and take the square root.
That is the quickest way.
So: square root.
1. no x term, or ( )² = k? ✓ square root
2 Get x² alone
To remove times 2, we divide both sides by 2.
2x22 = 322
32 divided by 2 is 16.
x2 = 16
3 Square root of both sides
x squared is 16.
So x is the square root of 16, or minus it.
Minus times minus is plus, so the negative one works too.
x² = k → x = √k or x = −√k
4 × 4 = 16, (−4) × (−4) = 16
4 times 4 is 16.
So x = 4 or x = −4.
x = 4 or x = −4
Careful!
Many people write only x = 4.
They lose the minus answer.
Careful: not only x = 4 ✗
4 Check
Let's check: put x = 4 into the left side.
x = 4: 2(4)2 = 32
We get 32, the same as the right side.
It works!
Now put x = −4 into the left side.
x = −4: 2(−4)2 = 32
We get 32 again, the same as the right side.
So both answers are right!
Let's look back.
First: choose the method.
Then: get x² alone.
Then: square root of both sides.
Last: check.
Answer
x = 4 or x = −4