# Thread: completing the square with an A-term co-efficient

1. ## completing the square with an A-term co-efficient

I am trying to complete the square, just for a quadratic equation, not for a graph. i had no problem with completing the square the first time around, but suddenly, i am getting all the review questions wrong and i dont know why! here is an example:

first, i cleared the co-efficient of the A term and came up with:

(i took half of 2 [which is 1] and squared it [which is 1], added to both sides)

(i rationalized and came up with):

the book says the answer is

where on earth did that -2 come from? all of the problems i have done have the wrong number in front of the plus/minus. i think it has something to do with the co-efficient of the A term, but i dont remember having to do anything with that. i know how to complete the square, i just dont know where that -2 came from. any insight?

2. Originally Posted by nikki33
I am trying to complete the square, just for a quadratic equation, not for a graph. i had no problem with completing the square the first time around, but suddenly, i am getting all the review questions wrong and i dont know why! here is an example:
2y^2+4y-3 = 0
first, i cleared the co-efficient of the A term and came up with:
y^2+2y = 3/2
y^2+2y+1 = 5/2
(i took half of 2 [which is 1] and squared it [which is 1], added to both sides)
(y+1)^2 = 5/2
y+1 = sqrt 5/2
The way you are writing your answers in this form gets a bit confusing. Let me just take it from this point.
$y + 1 = \pm \sqrt{\frac{5}{2}}$

$y + 1 = \pm \frac{\sqrt{10}}{2}$

$y = -1 \pm \frac{\sqrt{10}}{2}$

Adding the -1 as a fraction:
$y = -\frac{2}{2} \pm \frac{\sqrt{10}}{2}$

$y = \frac{-2 \pm \sqrt{10}}{2}$

-Dan

3. Hello,

y+1 = +- sqrt 5/2
Ok !

So $y=-1 \pm \sqrt{\frac 52}=-1 \pm \sqrt{\frac{10}{4}}=-1 \pm \frac{\sqrt{10}}{2}=\frac{-{\color{red}2} \pm \sqrt{10}}{2}$

4. im so sorry about the confusing squares and radicals. i have changed it, a little too late, but at least now i know how to do it! my apologies.

so, in terms of the -2 that is mystifying me, is it a -2 because the entire answer is under a 2 and if i let that -1 there, it would become -1/2? so i must change it to -2/2 (of course which is still -1) to keep the answer correct?(i hope the way im working this makes sense!) im sorry, im studying for finals and i think my head is too clogged . thank you for you time.

5. well, i guess the reason is that my answer,

would imply that the -1 is -1/2

and this answer:

implies that the -2/2 is the -1 that i originally came up with.

if i am incorrect, please let me know. and thanks for your time.