# Thread: Complete the Square

1. ## Complete the Square

Complete the square of the given function.

f(x) = x^2 - 6x

HINT GIVEN:

If f(x) = x^2 - 2x, then f(x) = (x^2 - 2x + 1) - 1 = (x - 1)^2 - 1.

I am looking for steps.

Sample:

Step 1: do this

Step 2: do that, etc.

RE:

-qbkr21

3. ## Tell me...

Where did the fraction (-6/2) come from?

4. If you have an expression, say
$x^2 + 3x$
that you need to complete the square of, consider the following:
$x^2 + 2ax + a^2 = (x + a)^2$

So we wish to add a number to our expression to put it in the above form.

So equate the coefficients of the linear terms:
$3 = 2a$

Thus
$a = \frac{3}{2}$

According to the prescription, then, we need to add an $a^2$ to our $x^2 + 3x$ to make it a perfect square. But what we add on one side, we must also subtract (so we're adding a net of zero to that side), thus:
$x^2 + 3x = x^2 + 3x + \left ( \frac{3}{2} \right ) ^2 - \left ( \frac{3}{2} \right ) ^2$

$= \left ( x + \frac{3}{2} \right ) ^2 - \left ( \frac{3}{2} \right ) ^2$

-Dan

5. Originally Posted by blueridge
Where did the fraction (-6/2) come from?
$x^2 - 6x$

When you complete the square you add (1/2) of the middle term squared.

So $\frac{6}{2} = 3$ and squared is 9.