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Help on C1 Completing the square?

The question is
Complete the square for the following quadratic expression

2x^2 - 6x + 5

Now the answer I have got is 2(x - 1.5x)^2 + 19/2

I've looked in the answer book and the answer there is 2(x - 1.5)^2 + 1/2

Can anyone tell me where i've gone wrong? I've looked through my answer but just can't see what i've done wrong.

Thanks :colondollar:
Reply 1
Avatar for Tompazr
Tompazr
11
- not +
Reply 2
Avatar for ilyking
ilyking
doesn't this produce an imaginary part?
(edited 13 years ago)
Reply 3
Avatar for Fabolous
Fabolous
2x^2 -6x + 5

divide bracket by 2 and then half b value (-6x)

so, 2(x-3/2) then (3/2)^2 multiply by 2 = 4.5

so, 2(x-3/2) +5 = 4.5

therefore, 2(x-3/2) + 0.5 = 0

Peace
Reply 4
Avatar for Larriant
Larriant
6
2x^2 - 6x + 5

2[x^2-3x] + 5
2[(x-1.5)^2 - 2.25)] +5
2(x-1.5)^2-4.5+5
2(x-1.5)^2 +0.5
That's if you just want to complete the square.
If you want to solve:
2(x-1.5)^2 =-0.5
x-1.5 = root -0.5/2
x=root (-0.5/2) + 1.5

Hope that helps. If you need any more help pm me.
(edited 13 years ago)
Are you sure it isn't -1/2?
Reply 6
Avatar for Larriant
Larriant
6
Original post by understandable
Are you sure it isn't -1/2?


It's +1/2.
Reply 7
Avatar for hash007
hash007
OP
15
Original post by Larriant
2x^2 - 6x + 5

2[x^2-3x] + 5
2[(x-1.5)^2 - 2.25)] +5
2(x-1.5)^2-4.5+5
2(x-1.5)^2 +0.5
That's if you just want to complete the square.
If you want to solve:
2(x-1.5)^2 =-0.5
x-1.5 = root -0.5/2
x=root (-0.5/2) + 1.5

Hope that helps. If you need any more help pm me.


Thanks :smile: I see where I went wrong, I put the +5 in the bracket as well instead of leaving it outside.
Think i've left my revision too late...
Reply 8
Avatar for ilyking
ilyking
Original post by hash007
Thanks :smile: I see where I went wrong, I put the +5 in the bracket as well instead of leaving it outside.
Think i've left my revision too late...


I usually bracket all of it and put everything inside and multiply everything by the coefficient of x^2 but it works either way as larrient suggested
Edit: Ignore that completely... :P
(edited 13 years ago)
Original post by hash007
The question is
Complete the square for the following quadratic expression

2x^2 - 6x + 5

Now the answer I have got is 2(x - 1.5x)^2 + 19/2

I've looked in the answer book and the answer there is 2(x - 1.5)^2 + 1/2

Can anyone tell me where i've gone wrong? I've looked through my answer but just can't see what i've done wrong.

Thanks :colondollar:


You've added (9/4) instead of subtracting it.

When you complete the square for x2+bx+cx^2 + bx + c, you reduce the x2+bxx^2 + bx part into (x+b2)\left(x+\frac{b}{2}\right), but they aren't equal; when we do this our answer is b2b^2 higher than it should be as when you expand (x+b)2(x+b)^2 you get x2+2bx+b2x^2 + 2bx + b^2, hence we subtract the b^2 term.

EDIT: Urgh, I started typing this about 30 minutes ago, stupid distractions xD
Reply 11
Avatar for hash007
hash007
OP
15
Original post by EEngWillow
You've added (9/4) instead of subtracting it.

When you complete the square for x2+bx+cx^2 + bx + c, you reduce the x2+bxx^2 + bx part into (x+b2)\left(x+\frac{b}{2}\right), but they aren't equal; when we do this our answer is b2b^2 higher than it should be as when you expand (x+b)2(x+b)^2 you get x2+2bx+b2x^2 + 2bx + b^2, hence we subtract the b^2 term.

EDIT: Urgh, I started typing this about 30 minutes ago, stupid distractions xD


Haha you're right, I think I should do some more examples to get the idea to stick :redface:
Original post by hash007
Haha you're right, I think I should do some more examples to get the idea to stick :redface:


Good plan. Practice makes perfect. I used to hate completing the square when I did C1, looking back I really don't know why! :tongue:

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