f(x) = x^2 + 2, find x when f(x) = 27

Step by step

The question

Question: find x when f(x) = 27 for f(x) = x² + 2.

f(x) = 27 means: the answer that comes out is 27.

We look for the x that goes in.

Careful!

It is not f(27).

27 is what comes out, not what goes in.

1 Write the equation

f(x) is x² + 2.

So x² + 2 = 27.

Now we solve it.

2 Get x² alone

There is no x term, so we get x² by itself.

To remove the + 2, we take away 2 on both sides.

27 − 2 = 25.

Now we have x² = 25.

3 Square root of both sides

x squared is 25.

So x is the square root of 25, or minus it.

Minus times minus is plus, so the negative one works too.

5 times 5 is 25.

So x = 5 or x = −5.

4 Check

Let's check: put 5 into f.

We get 27.

And −5 into f.

We get 27 too.

So f(5) = 27 and f(−5) = 27.

Both answers are right!

Let's look back.

First: write the equation.

Then: get x² alone.

Then: square root of both sides.

Last: check.