# Completing the square with fraction as coefficient of x^2

• Apr 27th 2013, 10:38 PM
Unreal
Completing the square with fraction as coefficient of x^2
Hi!

Complete the square for $\frac12x^2-x+3$

$\frac{-2}{2(1)}\,=\,1$

$\frac12(x^2 - 2x + 1 - 1) + 3$

$\frac12(x-1)^2 - 2$
• Apr 27th 2013, 10:50 PM
Prove It
Re: Completing the square with fraction as coefficient of x^2
You make life difficult on yourself if you skip steps. The first thing to do is to take out \displaystyle \begin{align*} \frac{1}{2} \end{align*} as a factor, then complete the square on everything left over, then multiply that factor back through.
• Apr 27th 2013, 11:27 PM
Unreal
Re: Completing the square with fraction as coefficient of x^2
$\frac{-2}{2(1)}\,=\,1$

$\frac12(x^2 - 2x) + 3$

$\frac12\left[(x^2 - 2x + 1 - 1) + 3\right]$

$\frac12(x-1)^2 - 1 + 3$

$\frac12(x-1)^2 + 2$
• Apr 27th 2013, 11:51 PM
Prove It
Re: Completing the square with fraction as coefficient of x^2
I'm not giving any more help until you learn to follow the instructions you've been given.
• Apr 28th 2013, 12:14 AM
Unreal
Re: Completing the square with fraction as coefficient of x^2
My solution is what I understand from the instructions given.

Quote:

Originally Posted by Prove It
The first thing to do is to take out $\frac12$ as a factor

Factoring $\frac12$ from the $x^2$ and $x$ terms: $\frac12\left[(x^2 - 2x + 6)\right]$

Quote:

Originally Posted by Prove It
then complete the square on everything left over

$\frac12(x^2 - 2x + 1 - 1 + 6)$

$\frac12\left[(x-1)^2 + 5\right]$

Quote:

Originally Posted by Prove It
then multiply that factor back through.

$\frac12(x-1)^2 + \frac52$
• Apr 28th 2013, 12:26 AM
Prove It
Re: Completing the square with fraction as coefficient of x^2
And this is correct. Well done.