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    I have attached a screenshot with part of the solution from my textbook.

    Unless I am missing something here, i'm under the impression that that taking 7.576 off of both sides of the quadratic leaves  -1.576 , not  1.576 .

    Is this a mistake in my textbook or am I missing something obvious?
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    (Original post by Illidan2)
    I have attached a screenshot with part of the solution from my textbook.

    Unless I am missing something here, i'm under the impression that that taking 7.576 off of both sides of the quadratic leaves  -1.576 , not  1.576 .

    Is this a mistake in my textbook or am I missing something obvious?
    You're right but you haven't noticed that the signs of the other terms have changed also. Your method will lead to this:

    -1.576 + 0.03f - 0.00006f^2=0

    Then if you move everything to the other side of the equation (or multiply both sides by -1) you will get the equation in the working.
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    (Original post by Illidan2)
    I have attached a screenshot with part of the solution from my textbook.

    Unless I am missing something here, i'm under the impression that that taking 7.576 off of both sides of the quadratic leaves  -1.576 , not  1.576 .

    Is this a mistake in my textbook or am I missing something obvious?
    It is -ve, but then they skipped it as they have multiplied through by -1.
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    (Original post by Notnek)
    You're right but you haven't noticed that the signs of the other terms have changed also. Your method will lead to this:

    -1.576 + 0.03f - 0.00006f^2=0

    Then if you move everything to the other side of the equation (or multiply both sides by -1) you will get the equation in the working.
    Oh right, I see. Why is everything multiplied by -1(reversing the signs) to move it to the other side? Why does everything have to be on the other side, rather than just taking 7.576 off of the right and left hand sides and having the right equal zero?

    Also, I have attached an example where I can't see this being done. I am puzzled. I didn't know I had to move everything to the right hand side. Why is this done in this instance, but the signs do not appear to change(and thus, everything does not appear to be moved to the right hand side) in the other example?
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    (Original post by Illidan2)
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    Oh right, I see. Why is everything multiplied by -1(reversing the signs) to move it to the other side? Why does everything have to be on the other side, rather than just taking 7.576 off of the right and left hand sides and having the right equal zero?

    Also, I have attached an example where I can't see this being done. I am puzzled. I didn't know I had to move everything to the right hand side. Why is this done in this instance, but the signs do not appear to change(and thus, everything does not appear to be moved to the right hand side) in the other example?
    You don't need to move everything to the other side - it's just what the first example did for some reason.
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    (Original post by Illidan2)
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    Oh right, I see. Why is everything multiplied by -1(reversing the signs) to move it to the other side? Why does everything have to be on the other side, rather than just taking 7.576 off of the right and left hand sides and having the right equal zero?

    Also, I have attached an example where I can't see this being done. I am puzzled. I didn't know I had to move everything to the right hand side. Why is this done in this instance, but the signs do not appear to change(and thus, everything does not appear to be moved to the right hand side) in the other example?
    Having a negative square is the kind of thing they don't want in solutions so they normally x everything by -1 to make the squared number a positive one.
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    Oh, I see! That's a relief. I thought I had not learned how to solve equations correctly. So if this has been done, does this have an impact on the answer? Would I be able to get the same answer with the opposite signs(not moving everything over to the other side)? I put this into a calculator(quadratic formula) and got two different values of f to the ones in the question, but this may simply be because I made an error entering the numbers.
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    (Original post by Illidan2)
    Oh, I see! That's a relief. I thought I had not learned how to solve equations correctly. So if this has been done, does this have an impact on the answer? Would I be able to get the same answer with the opposite signs(not moving everything over to the other side)? I put this into a calculator(quadratic formula) and got two different values of f to the ones in the question, but this may simply be because I made an error entering the numbers.
    You can multiply the equation by -1 and it won't affect your answer when you use the quadratic formula. If you got two different values then you must have made a mistake. If you're unsure you can post your working and we can check.

    What you should be thinking : multiplying an equation by -1 or moving everything to the other side doesn't change the equation since this is just manipulation that is allowed in algbera. So since the equation hasn't changed, the solutions won't change and so the quadratic formula must give you the same answer either way. Otherwise maths doesn't work
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    (Original post by Notnek)
    You can multiply the equation by -1 and it won't affect your answer when you use the quadratic formula. If you got two different values then you must have made a mistake. If you're unsure you can post your working and we can check.

    What you should be thinking : multiplying an equation by -1 or moving everything to the other side doesn't change the equation since this is just manipulation that is allowed in algbera. So since the equation hasn't changed, the solutions won't change and so the quadratic formula must give you the same answer either way. Otherwise maths doesn't work
    I tried again and I got the exact answers in the solution. Thank you! It's tough being so rusty with Maths, I wasn't aware of the "-1 rule", but i'll try to remember it from now on!
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    (Original post by Illidan2)
    I tried again and I got the exact answers in the solution. Thank you! It's tough being so rusty with Maths, I wasn't aware of the "-1 rule", but i'll try to remember it from now on!
    Just so you're clear, this isn't a special rule. You can multiply both sides of an equation by any number and the equation doesn't change. One of the first algebra rules you would have learnt is : "Do the same thing to the left as you do to the right".
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    Yes, this is what I was doing when I was taking 7.576 off of both sides, and it's what I do when dealing with any equation, do the same thing to both sides. It just confused me that they decided to multiply by -1, as it wasn't something that has ever occurred to me (the left-hand side has always been fine with me). But like, monkeyman said, it seems apparent that they simply wanted to keep their squared numbers positive.
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    Oh, another thing- why is 59.6 the answer here, and not 440.4? I understand that you may need some context to this mathematical model, to answer that, so i'll fill you in:

    "A fertiliser company uses a model to determine how the amount of fertiliser used, f kilograms per hectare, affects the grain yield g, measured in tonnes per hectare."

     g=6+0.03f-0.00006f

    b) One farmer currently uses 20 kilograms of fertiliser per hectare. How much more fertiliser would he need to use to increase his grain yield by 1 tonne per hectare?

    I can see how 59.6 is more likely to be the solution given that 20 kilograms was roughly an increase of 0.576 tonnes of grain per hectare from the base amount of 6 tonnes per hectare(when f=0), but I would prefer a more thorough understanding.
 
 
 
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