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<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>

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How would you solve...

x2 + 8x – 5 &#8801; (x + a)2 + b

help please :smile:

i have checked the mark scheme but its not very helpful
Reply 1
Avatar for HaNzY
HaNzY
2
its called completing the square. you have to halve the 8 (in 8x) and put (x+4)^2 and then you have to square that 4=16 and you have to always take this number away from the thing so make it a minus 16 and then minus 5(from the original quadratic) so -16-5 =-21 so the whole thing would read (x+4)^2-21 so a=4 and b=-21
Use use half of complete the square method, to the left into the one on the right.
Reply 3
Avatar for krazzie_ammo
krazzie_ammo
OP
ok cool i know how to complete the square, but what has that got to do with the right hand side of the equation because you are left with,

(x+4)^2-21 = (x + a)2 + b

dont you need to make the equation equal zero before you can work out a and b?
HaNzY
its called completing the square. you have to halve the 8 (in 8x) and put (x+4)^2 and then you have to square that 4=16 and you have to always take this number away from the thing so make it a minus 16 and then minus 5(from the original quadratic) so -16-5 =-21 so the whole thing would read (x+4)^2-21 so a=4 and b=-21


Perfectly explained...:wink:
Reply 5
Avatar for HaNzY
HaNzY
2
no no no, the three little lines in between the two equations means "can also be written as" they are the same equation so what i just told you was the answer
Reply 6
Avatar for HaNzY
HaNzY
2
thankyou very much :smile: i do try
Reply 7
Avatar for Mayson
Mayson
Actually the three lines mean 'is equal for ALL values of x'.

But you are right, it wants you to put the left hand side in the same form as the right hand side and hence find a and b. And completing the square is the way to do it in this case.
Reply 8
Avatar for HaNzY
HaNzY
2
oh well whatever, it explained that you need to write it in that form lolz :smile:
Reply 9
Avatar for krazzie_ammo
krazzie_ammo
OP
lol ok, thank you :smile:

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