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Math Help - Solving equations by completing the square.

  1. #1
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    Solving equations by completing the square.

    I am attempting to help my son with his homework and am completely stuck.. need to know how to solve the following:

    x2+4x=5 and show workings can anyone please help and explain to me in very simple terms?

    Thanks
    Carrie
    Last edited by mr fantastic; November 9th 2011 at 05:50 PM. Reason: Title.
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  2. #2
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    Re: solving equations by completing the square homework help... please help

    Quote Originally Posted by carrieh View Post
    I am attempting to help my son with his homework and am completely stuck.. need to know how to solve the following:

    x2+4x=5 and show workings can anyone please help and explain to me in very simple terms?

    Thanks
    Carrie
    What have you tried? Add 4 to both sides to get a perfect square on the left (and right for that matter)

    x^2 +4x + 4 = 5+4 \Longleftrightarrow (x+2)^2 = 9
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  3. #3
    MHF Contributor Amer's Avatar
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    Re: solving equations by completing the square homework help... please help

    to complete the square you add half of x coefficient squared
    for example

    x^2 + 12 x - 13 , (12/2)^2 = 36
    x^2 + 12 x + 36 - 36 -13
    (x+6)^2 - 49

    another one

    x^2 + 5 x + 4
    (5/2)^2 = 6.25

    x^2 + 5x + 6.25 - 6.25 + 4
    (x+ 2.5)62 - 2.25
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    Re: solving equations by completing the square homework help... please help

    Quote Originally Posted by carrieh View Post
    I am attempting to help my son with his homework and am completely stuck.. need to know how to solve the following:

    x2+4x=5 and show workings can anyone please help and explain to me in very simple terms?

    Thanks
    Carrie
    In general, if you have x^2+bx=c\,, you should change b to 2\left(\frac{b}{2}\right), and add \left(\frac{b}{2}\right)^2 to both sides of the equation. Then you have a perfect square on the left-hand side. (You have completed the square.)
    x^2+2\left(\frac{b}{2}\right)x+\left(\frac{b}{2} \right)^2=\left(x+\frac{b}{2}\right)^2
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    Re: solving equations by completing the square homework help... please help

    my equation is x^2+4x=5

    I need to solve the equation by completing the square. Using your example i am stuck already, sorry.. did say simple terms!!! Is half of my coefficent squared - 0.5^2? which would be 0.25? or is it the coefficient of x not x^2? (baby steps i know! sorry)
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  6. #6
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    Re: solving equations by completing the square homework help... please help

    Quote Originally Posted by carrieh View Post
    my equation is x^2+4x=5

    I need to solve the equation by completing the square. Using your example i am stuck already, sorry.. did say simple terms!!! Is half of my coefficent squared - 0.5^2? which would be 0.25? or is it the coefficient of x not x^2? (baby steps i know! sorry)
    The coefficient of x is the number next to x. In your question the coefficient of x is 4
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    Re: solving equations by completing the square homework help... please help

    so in x^2+4x=5 My coefficient is (4/2)^2 =4

    then don't understand where the 4 fits into my equation would it be x^2 + 4x + 4 -4 =5? Your equation does not show an = does this matter and does it affect the outcome?
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  8. #8
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    Re: solving equations by completing the square homework help... please help

    Quote Originally Posted by carrieh View Post
    so in x^2+4x=5 My coefficient is (4/2)^2 =4

    then don't understand where the 4 fits into my equation would it be x^2 + 4x + 4 -4 =5? Your equation does not show an = does this matter and does it affect the outcome?
    Yes although you can move that -4 over to the other side and change it's sign

    You should get x^2+4x+4 = 9 and since you have x^2 + 2\left(\dfrac{4x}{2}\right) + 2^2 you can factor it as per post 4 to get (x+2)^2 = 9
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    Re: solving equations by completing the square homework help... please help

    ok so now i have

    x^2 +4x +4 =9 (and i understand how we got there!)

    the way my sons maths book shows how to work it out is this:

    x^2 - 6x + 2 = 0
    add -2 to each side
    x^2 - 6x = -2
    add 9 to each side
    x^2 - 6x + 9 = -2+9 (I understand up until this part)
    (x-3)^2 = 7 (I do not know how to get it to this? sorry!
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    Re: solving equations by completing the square homework help... please help

    Have to run to take son canoeing, will be back about 9pm to check on answers and more than likely with more questions! Thanks so much for your help so far, i'm not the easiest to teach!!!
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  11. #11
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    Re: solving equations by completing the square homework help... please help

    Quote Originally Posted by carrieh View Post
    ok so now i have

    x^2 +4x +4 =9 (and i understand how we got there!)

    the way my sons maths book shows how to work it out is this:

    x^2 - 6x + 2 = 0
    add -2 to each side
    x^2 - 6x = -2
    add 9 to each side
    x^2 - 6x + 9 = -2+9 (I understand up until this part)
    (x-3)^2 = 7 (I do not know how to get it to this? sorry!
    They factorised the left hand side (does your son know how to factor a quadratic normally?) which was a perfect square. You can check by expanding (x-3)^2 using FOIL.

    Note that your equation is also in the form of a perfect square but, if you prefer, which two numbers sum to 4 and multiply to 4? The answer is 2 and 2 so you have x^2+4x+4 = (x+2)(x+2) = (x+2)^2 and of course this is equal to 9.

    Since you have (x+2)^2 = 9 you can take the square root: x+2 = \pm 3
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  12. #12
    Super Member Quacky's Avatar
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    Re: solving equations by completing the square homework help... please help

    Slightly different approach/explanation:

    Literally, drag everything onto one side:

    x^2+4x-5=0

    Halve the x coefficient, and bracket it:

    (x+2)^2

    Now, if we expand this, we get x^2+4x+4 which is not what we had originally. So we need to subtract 4 and 5 to get what we had originally, and this gives:

    (x+2)^2-4-5=0

    Then, we can rewrite the "spare" terms on the right:

    (x+2)^2=9

    And then by taking the square root of both sides, we're there!
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