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# Algebra help...QUADRATIC EQUATIONS ..completing the square..???? watch

1. Hi can any maths boffins assist a poor maths dunce with this one please?

I've had to do a level 3 maths course at work, but of a shock as sat GCSE maths in 1996 and only got a 'C'!

Anyway, this is one of the questions.

TAHIR HAS A REGULAR CYCLE TRAINING ROUTE THAT IS 60KM LONG. IF TAHIR CYCLES 3KMH SLOWER THAN HIS RACING SPEED,IT TAKES HIM 3 HOURS AND 20 MINUTES LONGER TO COMPLETE THE ROUTE.

A) WORK OUT TAHIR'S RACING SPEED. STATE IN WORDS WHAT ALGEBRAIC METHOD YOU ARE USING AT EACH STAGE.

C) EVALUATE ALL THREE METHODS FOR EFFICIENCY AND EFFECTIVENESS.

V^3 - 3V - 54 = 0
So how far have I got? Well the teacher gave us this quadratic equation above (still need to work out how I create an equation from the word problem, that's for another day! I've put it into the quadratic formula and factorised it and both have given me the answers V = 9 V = -6

I hope that's correct? Any idea how I can get the answers by 'completing the square'? Any other advise gratefully received.

Thank you
2. (Original post by outofblue)
Hi can any maths boffins assist a poor maths dunce with this one please?

I've had to do a level 3 maths course at work, but of a shock as sat GCSE maths in 1996 and only got a 'C'!

Anyway, this is one of the questions.

TAHIR HAS A REGULAR CYCLE TRAINING ROUTE THAT IS 60KM LONG. IF TAHIR CYCLES 3KMH SLOWER THAN HIS RACING SPEED,IT TAKES HIM 3 HOURS AND 20 MINUTES LONGER TO COMPLETE THE ROUTE.

A) WORK OUT TAHIR'S RACING SPEED. STATE IN WORDS WHAT ALGEBRAIC METHOD YOU ARE USING AT EACH STAGE.

C) EVALUATE ALL THREE METHODS FOR EFFICIENCY AND EFFECTIVENESS.

V^3 - 3V - 54 = 0
So how far have I got? Well the teacher gave us this quadratic equation above (still need to work out how I create an equation from the word problem, that's for another day! I've put it into the quadratic formula and factorised it and both have given me the answers V = 9 V = -6

I hope that's correct? Any idea how I can get the answers by 'completing the square'? Any other advise gratefully received.

Thank you
If you have never done completing the square method, I am attaching information on how to do it.
Attached Images
3. Scan0013.pdf (243.6 KB, 78 views)
4. Where did you get that equation from? It's not related to the problem and is a cubic, not a quadratic. You can't complete the square on a cubic the same way you would with a quadratic.
Use s=vt on the information you've been given.
5. (Original post by morgan8002)
Where did you get that equation from? It's not related to the problem and is a cubic, not a quadratic. You can't complete the square on a cubic the same way you would with a quadratic.
Use s=vt on the information you've been given.
e
The original poster said that it was a quadratic so I assumed that the v^3 was a typo.

My humble apologies.
6. (Original post by RosaA)
...
(Original post by maggiehodgson)
e
The original poster said that it was a quadratic so I assumed that the v^3 was a typo.

My humble apologies.
You might be right.
7. (Original post by morgan8002)

You might be right.

Perhaps I am, considering that the subject/title of the post was :

Algebra help...QUADRATIC EQUATIONS ..completing the square..????

I felt awful for a minute but I don't feel so foolish now.
8. (Original post by morgan8002)
Where did you get that equation from? It's not related to the problem and is a cubic, not a quadratic. You can't complete the square on a cubic the same way you would with a quadratic.
Use s=vt on the information you've been given.

We've only had 2 lessons on this course and I copied off the whiteboard last lesson, was under the impression it was the equation to the said word problems.

YIKES! I'm really worried now, I've wasted a lot of the weekend working on this assignment and it looks like all I've done is write rubbish.

:-(

Thank you to those who've tried to help me.
9. (Original post by outofblue)
We've only had 2 lessons on this course and I copied off the whiteboard last lesson, was under the impression it was the equation to the said word problems.

YIKES! I'm really worried now, I've wasted a lot of the weekend working on this assignment and it looks like all I've done is write rubbish.

:-(

Thank you to those who've tried to help me.
Don't worry, the 2 answers you wrote at the beginning were right, but the word problem gives V^2 - 3V - 54 = 0 which does give you V = 9 or -6 as you said above. You must have just copied down the equation wrong and wrote V^3 instead of V^2, quadratics only go up to squared terms, nothing higher.

As for the original thing you asked, completing the square just makes it so that the variable only appears once in the equation, making it easier to solve. In this case:

V^2 - 3V = (V - 3/2)^2 - (3/2)^2

With only one V term there, you just need to do some rearranging to solve it (Look at the first bit in the attachment to maggie's first post).

There's also one important thing for this sort of question I don't see mentioned yet, do both your answers make sense as speeds?
Don't worry, the 2 answers you wrote at the beginning were right, but the word problem gives V^2 - 3V - 54 = 0 which does give you V = 9 or -6 as you said above. You must have just copied down the equation wrong and wrote V^3 instead of V^2, quadratics only go up to squared terms, nothing higher.

As for the original thing you asked, completing the square just makes it so that the variable only appears once in the equation, making it easier to solve. In this case:

V^2 - 3V = (V - 3/2)^2 - (3/2)^2

With only one V term there, you just need to do some rearranging to solve it (Look at the first bit in the attachment to maggie's first post).

There's also one important thing for this sort of question I don't see mentioned yet, do both your answers make sense as speeds?
Thank you so much Adam. I feel a bit better now :-) No I see what you mean, so although there's 2 answers to a quadratic we only take 1 answer in this case??? Only 9 makes sense? Gonna watch a few videos on youtube re algebra for an hour and then watch tv for a bit & chill out!!!!

Thanks again to everybody for the help.
11. (Original post by outofblue)
Thank you so much Adam. I feel a bit better now :-) No I see what you mean, so although there's 2 answers to a quadratic we only take 1 answer in this case??? Only 9 makes sense? Gonna watch a few videos on youtube for an hour and then watch tv for a bit & chill out.

Thanks again to everybody for the help.
No problem, and yeah you're right. Usually for questions that have this sort of trick, you'd write down both solutions to the equation then point out that one doesn't make sense as an actual answer to the question, in this case a negative speed, leaving you with V = 9km/h.
12. (Original post by outofblue)
Thank you so much Adam. I feel a bit better now :-) No I see what you mean, so although there's 2 answers to a quadratic we only take 1 answer in this case??? Only 9 makes sense? Gonna watch a few videos on youtube re algebra for an hour and then watch tv for a bit & chill out!!!!

Thanks again to everybody for the help.
visit maths again ...

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