Rewrite the equation by completing the square. 2x^2 – 3x-5=0

Question

Rewrite the equation by completing the square.
2x^2 – 3x-5=0

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Rylee 2 weeks 2021-10-03T11:15:01+00:00 1 Answer 0

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    2021-10-03T11:16:32+00:00

    Answer:

    2[(x – 3/4)^2 – 49/16]

    Step-by-step explanation:

    Factor 2x^2 – 3x-5=0 as follows:

    2x^2 – 3x-5=0 = 2(x^2 – (3/2) – 5/2)

    Now focus on  x^2 – (3/2)x – 5/2 alone.  

    To complete the square, take half of the coeficient of x:  (1/2)(-3/2, or

    -3/4.  Now square this, obtaining 9/16.

    Going back to  x^2 – (3/2)x – 5/2, add in 9/16 and then subtract 9/16:

    x^2 – (3/2)x + 9/16 – 9/16 -5/2

    Rewrite x^2 – (3/2)x + 9/16 as the square of a binomial:  (x – 3/4)^2

    Then we have:  (x – 3/4)^2 – 9/16 – 5/2, or

                             (x – 3/4)^2  – 9/16 – 40/16, or    

                             (x – 3/4)^2 – 49/16

    Now go back to the original equation, 2x^2 – 3x-5=0, recall that this is equivalent to   2(x^2 – (3/2) – 5/2) .  Replace  x^2 – (3/2) – 5/2)  with

    (x – 3/4)^2 – 49/16, obtaining 2[(x – 3/4)^2 – 49/16]

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