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Algebra B

posted by on .

x^2 - 5/2x + 25/16 = -4 + 25/16
= (x-5/4)^2 = -64/16 + 25/16
= (x-5/4)^2 = -39/16

Would someone please explain how we arrived at

(x - 5/4)^2 = -64/16 + 25/16 from

x^2 - 5/2x + 25/16 = -4 + 25/16

Thanks in advance for your help.

  • Algebra B - ,

    Which side (left or right) is puzzling?

  • Algebra B - ,

    The left, Thanks

  • Algebra B - ,

    OK,
    (x-5/4)^2
    = (x-5/4)(x-5/4)
    multiplying (remember FOIL--first, outer, inner, last)

    = x^2 -(5/4)(x) - (5/4)(x) + (5/4)^2
    = x^2 - (10/4)(x) + (5^2)/(4^2)
    = x^2 -(5/2)(x) + (25)/(16)

    Does that help?

  • Algebra B - ,

    Oh, reverse FOIL!

    Thank you.

  • Algebra B - ,

    You're welcome, but I am not sure what you mean by reverse FOIL.

    First terms: x and x
    Outer terms: x and -5/4
    Inner terms: -5/4 and x
    Last terms : -5/4 and -5/4

    I just want to be sure you have a good understanding about the order.

  • Algebra B - ,

    Yes, You explained it very well. Thanks for taking the time.

  • Algebra B - ,

    You are very welcome.

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