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Math Help - Complete the square

  1. #1
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    Complete the square

    10v2−15v =27+4v2−6v
    SOS-
    the answer is
    v=3 or -3/2

    show the calculation please!
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Complete the square

    Quote Originally Posted by edmundyong View Post
    10v2−15v =27+4v2−6v
    SOS-
    the answer is
    v=3 or -3/2

    show the calculation please!
    10v^2 - 15v = 27 + 4v^2 - 6v

    6v^2 - 9v = 27

    I'm sure you've gotten this far.

    What does "complete the square" mean? We need to add a number to both sides of the equation such that the LHS is a perfect square. My first suggestion is to divide through by 6 to make the coefficient of v^2 one. (This is not necessary, but I find it makes the problem simpler.)

    v^2 - \frac{9}{6}v = \frac{27}{6}

    v^2 - \frac{3}{2}v = \frac{9}{2}

    We need to find a number to add to the LHS to make it a perfect square. The only number we can use is the coefficient of the linear term: 3/2. What does that tell us about the number we must add? Check your text and see how far you can get from here.

    -Dan
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: Complete the square

    Here is another approach to completing the square, arrange the equation as:

    2v^2-3v=9

    Multiply through by 4 times the coefficient of the squared term, which is 8 and then add the square of the coefficient of the linear term which is 9:

    16v^2-24v+9=72+9

    (4v-3)^2=9^2

    Can you finish?
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  4. #4
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    Re: Complete the square

    (v- a)^2= v^2- 2av+ a^2 You can write 10v^2−15v =27+4v^2−6v as 10v^2- 15v- (4v^2- 6v)= 6v^2- 9v= 6(v^2- (3/2)v=  27.

    Now compare v^2- (2/3)v with v^2- 2av. What is "a"? What is a^2?
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