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# completing the square Watch

1. i thought i done this correctly but according to the mark scheme, i did not...

the question asks: express 5x^2 + 20x - 8 in the form p(x+q)^2 + r.
i got 5(x+4)^2 - 95
but the mark scheme says, 5(x+2)^2 - 28

i dont understand this!
2. Lets see..

complete the square from there.
this may help:

it may look complex, but its quite simple. just put the values in and it should work out. The answer given is correct.
3. Its been a while since I had to do this but....

So it has to be (x+p) - 20 divided by 5 is 4, then to complete the square you need to divide this number by 2 to put it in the brackets.

(x+2)^2 - then if you multiply this out the c value you get is 4. Multiply this by the 5 which sits outside the brackets and you get 20. You need -8 so the difference is -28 for the c value.

This then gives the y=5(x+2)^2 -28

Hope this explains it clearly.
4. 5x^2 + 20x - 8 in the form p(x+q)^2 + r.

So,

(5x + 10)^2 - 20 - 8

= (5x + 10)^2 - 28

= 5(x + 2)^2 - 28

p = 5
q = 2
r = 28

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Updated: November 28, 2010
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