Turn on thread page Beta

Can you explain the solution to this Completing The Square related question please? watch

    • Thread Starter
    Offline

    11
    ReputationRep:
    I have the solution (at bottom of this message).

    I know how to solve the equation (part 2 of the question), but I don't understand how you would go abnout solviong it and looking art the solution, I don't get why you would do each section and what each section is doing. I would never be able to do it in an exam as I don't understand the method.

    Please can you explain it to me? (I know what is meant by p, q, and r when completing the square).

    Name:  Screenshot_35.png
Views: 52
Size:  33.2 KB
    Thanks, appreciate it!
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by blobbybill)
    I have the solution (at bottom of this message).

    I know how to solve the equation (part 2 of the question), but I don't understand how you would go abnout solviong it and looking art the solution, I don't get why you would do each section and what each section is doing. I would never be able to do it in an exam as I don't understand the method.

    Please can you explain it to me? (I know what is meant by p, q, and r when completing the square).


    Thanks, appreciate it!
    The wanted form has been expanded fully in terms of p, q and r. Then we know the coefficients of x^2, x and the constant must be the same in order for the equation to hold. So you make up some equations by considering each coefficient individually and solve for them.
    Offline

    21
    ReputationRep:
    (Original post by blobbybill)
    I have the solution (at bottom of this message).

    I know how to solve the equation (part 2 of the question), but I don't understand how you would go abnout solviong it and looking art the solution, I don't get why you would do each section and what each section is doing. I would never be able to do it in an exam as I don't understand the method.

    Please can you explain it to me? (I know what is meant by p, q, and r when completing the square).
    For the expressions to be equal for all values of x, they have to be the same expression. You therefore expand the RHS to get a quadratic in x and set each of the coefficients equal to the same one on the LHS.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by RDKGames)
    The wanted form has been expanded fully in terms of p, q and r. Then we know the coefficients of x^2, x and the constant must be the same in order for the equation to hold. So you make up some equations by considering each coefficient individually and solve for them.
    How do we know the coefficients of x^2 and x? And what do you mean by you make up some equations by considering each coefficient individually? I get that we know p=3, (because 3x^2), and you expand the RHS to get a quadratic. But then why do you need to get that quadratic? What does it mean by stuff like "Comparing x: 2pq = 12"?

    I don't have a clue really what each step of the solution means and why you do each step.

    (Original post by RogerOxon)
    For the expressions to be equal for all values of x, they have to be the same expression. You therefore expand the RHS to get a quadratic in x and set each of the coefficients equal to the same one on the LHS.
    Why do you want to get a quadratic "in x" on the RHS? What does "in x" mean? What dou you mean by "set each of the coefficients equal to the same one" on the LHS"?

    Please can you explain each step as basic as possible, I don't get this question.

    Thanks!
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by blobbybill)
    How do we know the coefficients of x^2 and x?
    Because on the LHS they are 3, 12 and 5 respectively therefore they must be 3, 12 and 5 on the RHS too.

    And what do you mean by you make up some equations by considering each coefficient individually?
    I mean that once you have the RHS in the form of Ax^2+Bx+C (which is the same form as the LHS) you can compare the coefficients between LHS and RHS

    So 3=A. 12=B and 5=C for whatever your A, B and C are in terms of p, q and r. So then you can solve for p, q and r.
    I get that we know p=3, (because 3x^2), and you expand the RHS to get a quadratic. But then why do you need to get that quadratic? What does it mean by stuff like "Comparing x: 2pq = 12"?
    Again, coefficients must be the same so the coefficient of x must be the same on both sides hence 2pq=12.

    I don't have a clue really what each step of the solution means and why you do each step.
    Time to learn something new then.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by RDKGames)
    Because on the LHS they are 3, 12 and 5 respectively therefore they must be 3, 12 and 5 on the RHS too.



    I mean that once you have the RHS in the form of Ax^2+Bx+C (which is the same form as the LHS) you can compare the coefficients between LHS and RHS

    So 3=A. 12=B and 5=C for whatever your A, B and C are in terms of p, q and r. So then you can solve for p, q and r.


    Again, coefficients must be the same so the coefficient of x must be the same on both sides hence 2pq=12.



    Time to learn something new then.
    I'm guessing that we know pq^2 + r is the constant because there is no x in there? And the form of a quadratic is ax^2 + bx + c, so it is the constant, c, because there is no x in that part of the equation? So basically wherever there isn't an x, that is the constant?

    Also, when you say the "coefficients must be the same so the coefficient of x must be the same on both sides, hence 2pq=12", what do you mean when you say the coefficient of x must be the same? Do you mean the bit before x, so 2pq(x) and 12(x)?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by blobbybill)
    I'm guessing that we know pq^2 + r is the constant because there is no x in there? And the form of a quadratic is ax^2 + bx + c, so it is the constant, c, because there is no x in that part of the equation? So basically wherever there isn't an x, that is the constant?
    Correct - the constants can otherwise be referred to as coefficients of x^0 though you should already know this.

    Also, when you say the "coefficients must be the same so the coefficient of x must be the same on both sides, hence 2pq=12", what do you mean when you say the coefficient of x must be the same? Do you mean the bit before x, so 2pq(x) and 12(x)?
    Yes that is the coefficient, you should not forget that.



    Posted from TSR Mobile
 
 
 
Poll
A-level students - how do you feel about your results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.