# Math Help - Completing The Square

1. ## Completing The Square

Do people know how to complete the square

For Example:
3x2 - 15x + 18 = 0

(Note: 3x2 means 3x squared)

2. pull out the common factor of 3, which leaves you:

3(x^2 - 5x + 6) = 0 ----> 3(x-3)(x-2) = 0

x= 3 and x=2

3. OMG!! Mathless i absolutely love u!!!!

4. Originally Posted by liveboon
Do people know how to complete the square

For Example:
3x2 - 15x + 18 = 0

(Note: 3x2 means 3x squared)
$3x^2 - 15x + 18 = 0$

$3(x^2 - 5x + 6) = 0$

$3\left[x^2 - 5x + \left(-\frac{5}{2}\right)^2 - \left(-\frac{5}{2}\right)^2 + 6\right] = 0$

$3\left[\left(x - \frac{5}{2}\right)^2 - \frac{25}{4} + \frac{24}{4}\right] = 0$

$3\left[\left(x - \frac{5}{2}\right)^2 - \frac{1}{4}\right] = 0$

$3\left(x - \frac{5}{2}\right)^2 - \frac{3}{4} = 0$.

5. P.S. Someone please lock this thread - there's no need for outbursts like that!

6. Originally Posted by liveboon
Do people know how to complete the square

For Example:
3x2 - 15x + 18 = 0

(Note: 3x2 means 3x squared)

In general, $ax^2+bx+c=a\left(x+\frac{b}{2a}\right)^2 +c-\frac{b^2}{4a}$ , and perhaps you can recognize the term $c-\frac{b^2}{4a}=-\frac{\Delta}{4a}\,,\,\,\Delta=$ the quadratic's discriminant.

So yes, I think some people know how to complete the square.

Tonio

7. Originally Posted by Mathless
pull out the common factor of 3, which leaves you:

3(x^2 - 5x + 6) = 0 ----> 3(x-3)(x-2) = 0

x= 3 and x=2

I'm afraid this is not what the OP asked for, though she/he seems to be unaware of it. What you did here is to factor the quadratic, which is very useful to calculate its roots, for example, but it's not completing the square.

Tonio

8. I've seen enough happen here in this thread. Now that the question has been answer, there is no need to continue posting here.