# Completing the square

• Apr 27th 2013, 10:58 PM
Unreal
Completing the square
Hi!

Apparently this is wrong, how do I get the correct form?

Complete the square for $y = -x^2-2x$

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

$-(x^2-2x) = -(x^2-2x+1)-1$

$-(x+1)^2-1$
• Apr 27th 2013, 11:15 PM
Prove It
Re: Completing the square
\displaystyle \begin{align*} y &= -x^2 - 2x \\ &= - \left( x^2 + 2x \right) \\ &= - \left[ x^2 + 2x + 1^2 - 1^2 \right] \\ &= - \left[ \left( x + 1 \right) ^2 - 1 \right] \\ &= - \left( x + 1 \right) ^2 + 1 \end{align*}
• Apr 27th 2013, 11:40 PM
Unreal
Re: Completing the square
Why is it necessary to factor out the negative 1?

$- \left[ x^2 + 2x + 1^2 - 1^2 \right]$
Could this be written as: $- \left[ x^2 + 2x + 1^2\right] - 1^2$ OR $- \left[ x^2 + 2x + 1^2\right] - 1^2 + 0$?
• Apr 27th 2013, 11:44 PM
Prove It
Re: Completing the square
To complete the square you require that your coefficient of \displaystyle \begin{align*} x^2 \end{align*} is 1, so if your coefficient is something different, you have to take it out as a factor and then complete the square on the leftover stuff.