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Complete The Square Question

Complete the square and please show me the working out as I am confused on how does the answer get the +10 as the rest I understand

5x^2-20x+30

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Original post by Daydreamer3
Complete the square and please show me the working out as I am confused on how does the answer get the +10 as the rest I understand

5x^2-20x+30


It is best to post your working so we can correct it.. otherwise it is just giving you the answer

You must have done almost all of it right anyway, I suspect it is just the part outside the brackets.

Please post your working :h:
Original post by SeanFM
It is best to post your working so we can correct it.. otherwise it is just giving you the answer

You must have done almost all of it right anyway, I suspect it is just the part outside the brackets.

Please post your working :h:


5(x^2-4)+30
5[(x-2)]^2-4+30
5[(x-2)]^2+16

OR

5[x^2-4x+6)

I dont even know what I did aha.... :/
Original post by Daydreamer3
5(x^2-4)+30
5[(x-2)]^2-4+30
5[(x-2)]^2+16

OR

5[x^2-4x+6)

I dont even know what I did aha.... :/


Okay, side question that will help (your last line is the correct way)

How do you complete the square for x^2 - 4x + 6?
Original post by SeanFM
Okay, side question that will help (your last line is the correct way)

How do you complete the square for x^2 - 4x + 6?


(x-2)^2-4+6

(x-2)^2+2
Original post by Daydreamer3
(x-2)^2-4+6

(x-2)^2+2


Good, so what is 5x^2 - 20x + 30 in completed square form, using the answer you have just given me?
Original post by SeanFM
Good, so what is 5x^2 - 20x + 30 in completed square form, using the answer you have just given me?


ummmm...

5(x-2)^2-4+6??

Can you please just tell me instead haha

Is it supposed to be 4+6 I dont know......!
Original post by Daydreamer3
ummmm...

5(x-2)^2-4+6??

Can you please just tell me instead haha

Is it supposed to be 4+6 I dont know......!


If you are asked to complete the square for 5x^2 - 20x + 30 which you have rewritten as 5(x^2 -4x + 6)


and you know that the completed square of (x^2 - 4x + 6) is (x-2)^2 + 2..

then the completed square of 5(x^2 - 4x + 6) = 5(x-2)^2 + ....
Original post by SeanFM
If you are asked to complete the square for 5x^2 - 20x + 30 which you have rewritten as 5(x^2 -4x + 6)


and you know that the completed square of (x^2 - 4x + 6) is (x-2)^2 + 2..

then the completed square of 5(x^2 - 4x + 6) = 5(x-2)^2 + ....


Yes I know it is +10 but what I dont understand is where it has come from.
Can you just please tell me the answer we have spent too long working this out ahah :tongue:
Original post by Daydreamer3
Yes I know it is +10 but what I dont understand is where it has come from.
Can you just please tell me the answer we have spent too long working this out ahah :tongue:


It has come from multiplying the whole thing by 5...

I'll pick up with my previous post and then if you are still stuck then ask :h:

(I know there is a slightly different method where you take out the 'a' in ax^2 + bx +c and divide through by it etc etc)

If the completed square of x2−4x+6=(x−2)2+2 x^2 - 4x + 6 = (x-2)^2 +2 and 5x2−20x+30 5x^2 - 20x + 30 is 5 times that, then the completed square of that is simply 5×((x−2)2+2)=5×((x−2)2)+(5×2)=5(x−2)2+10 5\times((x-2)^{2} + 2) = 5 \times( (x-2)^2) + (5 \times 2) = 5(x-2)^2 + 10
(edited 7 years ago)
Original post by SeanFM
It has come from multiplying the whole thing by 5...

I'll pick up with my previous post and then if you are still stuck then ask :h:

(I know there is a slightly different method where you take out the 'a' in ax^2 + bx +c and divide through by it etc etc)

If the completed square of x2−4x+6=(x−2)2+2 x^2 - 4x + 6 = (x-2)^2 +2 and 5x2−20x+30 5x^2 - 20x + 30 is 5 times that, then the completed square of that is simply 5×((x−2)2+2)=5×((x−2)2)+(5×2)=5(x−2)2+10 5\times((x-2)^{2} + 2) = 5 \times( (x-2)^2) + (5 \times 2) = 5(x-2)^2 + 10


Can you please just show the working out directly from 5x^2-20x+30 instead of using the other form as that would be more helpful.
Original post by Daydreamer3
Can you please just show the working out directly from 5x^2-20x+30 instead of using the other form as that would be more helpful.

5x²-20x+30
5(x²-4x)+30
5[(x-2)²-4]+30
5(x-2)²+30-20
5(x-2)²+10
Original post by Daydreamer3
Can you please just show the working out directly from 5x^2-20x+30 instead of using the other form as that would be more helpful.


Let me know which bit of what I have shown is confusing.. if not just read it over and see if you get it :smile:

I'm not sure what method you're used to as you haven't shown one for an ax term, but you could consider the first two terms and express it as 5(x^2 - 4), which is 5(x-2)^2. and then see that, when expanded, that is equal to 5(x^2 - 4x + 4) which is 5x^2 - 20x + 20 which is 10 less than the original expression, so we'd have to add 10 to the bold expression to give 5(x-2)^2.
Here u are, hard to see on pc
IMG_5091.jpg473.5KB
Original post by metrize
5x²-20x+30
5(x²-4x)+30
5[(x-2)²-4]+30
5(x-2)²+30-20
5(x-2)²+10


Oh okayy so you had to multiply the 5 by the 4 I think, thank you! :smile:
Original post by SeanFM
Let me know which bit of what I have shown is confusing.. if not just read it over and see if you get it :smile:

I'm not sure what method you're used to as you haven't shown one for an ax term, but you could consider the first two terms and express it as 5(x^2 - 4), which is 5(x-2)^2. and then see that, when expanded, that is equal to 5(x^2 - 4x + 4) which is 5x^2 - 20x + 20 which is 10 less than the original expression, so we'd have to add 10 to the bold expression to give 5(x-2)^2.


Thank you so much for the help! :smile:
Original post by whowannadate
Here u are, hard to see on pc


Thank youu!! :smile:
Lmao, the only way you'll truly understand the +10 is if you try and figure it out yourself rather than having someone feed you the information. Better to correct your mistakes yourself

Posted from TSR Mobile
Original post by Daydreamer3
Thank youu!! :smile:


http://www.mathsgenie.co.uk/gcse.html
Original post by Moltenmo
Lmao, the only way you'll truly understand the +10 is if you try and figure it out yourself rather than having someone feed you the information. Better to correct your mistakes yourself

Posted from TSR Mobile


Yeah well then I could have just made up anything to get the answer even if wasnt the correct method.... :tongue:

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