Step by step
The question
Question: choose a method and solve x² = 49.
x2 = 49
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 Square root of both sides
x squared is 49.
So x is the square root of 49, or minus it.
Minus times minus is plus, so the negative one works too.
x² = k → x = √k or x = −√k
7 × 7 = 49, (−7) × (−7) = 49
7 times 7 is 49.
So x = 7 or x = −7.
x = 7 or x = −7
Careful!
Many people write only x = 7.
They lose the minus answer.
Careful: not only x = 7 ✗
3 Check
Let's check: put x = 7 into the left side.
x = 7: 72 = 49
We get 49, the same as the right side.
It works!
Now put x = −7 into the left side.
x = −7: (−7)2 = 49
We get 49 again, the same as the right side.
So both answers are right!
Let's look back.
First: choose the method.
Then: square root of both sides.
Last: check.
Answer
x = 7 or x = −7