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11 November, 05:14

What equation results from completing the square and then factoring?

x^2-10x=46

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Answers (1)
  1. 11 November, 09:12
    0
    Move all like term to the same side

    x^2-10x-46=0

    1. The expression x^2-10x-46 fits into the from ax^2+2b+c, where:

    a=1, b=-10 and c=-46

    2. Introduce the constant, k, which is 25 in our case

    Let k = (b/-2a) ^2

    From the earlier step, we know that a=1 and b=-10

    Therefore, k = (-10/2*1) ^2 = 25

    x^2-10x+25-25-46=0

    3. Use square of difference: (a-b) ^2=a^2-2ab+b^2

    (x-5) ^2-25-46=0

    4. Simplify

    (x-5) ^2-71=0

    5. Substitute back into the original equation

    (x-5) ^2-71=0

    6. Add 71 on both sides

    (x-5) ^2=71

    7. Take the square root of both sides

    x-5=plus minus sqrt (71)

    8. Add 5 to both sides

    x = sqrt (71) + 5 or - sqrt (71) + 5
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