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C1- Completing the square

heya i would be gratefl if anyone could help me out with these questions

1)x2(squared)-3x-5=0

2)2x2-7=4x

3)4x2-x=8

4)15-6x-2x2=0

basically these do go into fractions and i kind of got confused when the teacher was explaining it, he did a funny methods i hadnt been taught

Any help much appreciated
Reply 1
Avatar for nuodai
nuodai
17
The methods are exactly the same whether you're using fractions or not.

If you have something like 3x2+4x+1=03x^2+4x+1=0 then you can take out the factor of 3 to get 3(x2+43x+13)=03 \left( x^2 + \dfrac{4}{3}x + \dfrac{1}{3} \right) = 0. Then you can complete the square on what's inside the bracket separately, and multiply through by 3 at the end.

If the coefficient of x2x^2 is negative, multiply through by -1 as well.
Reply 2
Avatar for kacey.flanagan
kacey.flanagan
OP
Thank you , see i was going wrong because i got the denominator and numerator wrong thanks, do you always put b(second digit) before a(first digit) in turns on the numerator
Reply 3
Avatar for emma363
emma363
14
nuodai
The methods are exactly the same whether you're using fractions or not.

If you have something like 3x2+4x+1=03x^2+4x+1=0 then you can take out the factor of 3 to get 3(x2+43x+13)=03 \left( x^2 + \dfrac{4}{3}x + \dfrac{1}{3} \right) = 0. Then you can complete the square on what's inside the bracket separately, and multiply through by 3 at the end.

If the coefficient of x2x^2 is negative, multiply through by -1 as well.


This isn't my thread but can I borrow you a second?
I've got to complete 5x2+x−35x^2 + x -3 and i've got to 5(x2+15x−35)5 ( x^2 + \dfrac{1}{5}x - \dfrac{3}{5} ) and now i'm kinda stuck...
can you tell me what I do next please, thankyou :biggrin:
(edited 13 years ago)
Reply 4
Avatar for nuodai
nuodai
17
emma363
This isn't my thread but can I borrow you a second?
I've got to complete 5x2+x−35x^2 + x -3 and i've got to 5(x2+15x−35)5 ( x^2 + \dfrac{1}{5}x - \dfrac{3}{5} ) and now i'm kinda stuck...
can you tell me what I do next please, thankyou :biggrin:

Look at x2+15x−35x^2 + \dfrac{1}{5}x - \dfrac{3}{5} separately and complete the square on that in exactly the same way that you normally would -- don't let the fractions confuse you. Then put it back into the equation (i.e. multiply through by the 5 that you took out) and you're done.
Reply 5
Avatar for emma363
emma363
14
nuodai
Look at x2+15x−35x^2 + \dfrac{1}{5}x - \dfrac{3}{5} separately and complete the square on that in exactly the same way that you normally would -- don't let the fractions confuse you. Then put it back into the equation (i.e. multiply through by the 5 that you took out) and you're done.

okay cheers :smile:

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