Step by step
The question
Question: find x when f(x) = 25 for f(x) = 3x² − 2.
f(x) = 25 means: the answer that comes out is 25.
We look for the x that goes in.
Careful!
It is not f(25).
25 is what comes out, not what goes in.
1 Write the equation
f(x) is 3x² − 2.
So 3x² − 2 = 25.
Now we solve it.
2 Get x² alone
There is no x term, so we get x² by itself.
To remove the − 2, we add 2 on both sides.
25 + 2 = 27.
Now we have 3x² = 27.
To remove times 3, we divide both sides by 3.
27 divided by 3 is 9.
3 Square root of both sides
x squared is 9.
So x is the square root of 9, or minus it.
Minus times minus is plus, so the negative one works too.
3 times 3 is 9.
So x = 3 or x = −3.
4 Check
Let's check: put 3 into f.
We get 25.
And −3 into f.
We get 25 too.
So f(3) = 25 and f(−3) = 25.
Both answers are right!
Let's look back.
First: write the equation.
Then: get x² alone.
Then: square root of both sides.
Last: check.