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24 December, 08:59

Solve the equation by completing the square. Round to the nearest hundredth if necessary. 2x^2-4x=5

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  1. 24 December, 09:09
    0
    x = 2.87 and - 0.87

    Step-by-step explanation:

    Rewrite 2x^2-4x=5 to make it easier to apply "completing the square:"

    2 (x^2 - 2x) = 5/2

    Then complete the square, putting all work inside parentheses:

    1) the coefficient of the x term is - 2. Take half of that: we get - 1.

    2) square this result; we get + 1.

    3) Add this square to x^2 - 2x, and then subtract it from the sum:

    x^2 - 2x + 1 - 1

    4) Rewrite the original 2 (x^2 - 2x) = 5/2 as:

    2 (x^2 - 2x + 1 - 1) = 5.

    Note that x^2 - 2x + 1 can be rewritten as the square of a binomial: (x - 1) ^2.

    Then we have: 2 (x - 1) ^2 - 2 = 5, or

    2 (x - 1) ^2 = 7, or

    (x - 1) ^2 = 7/2

    5. Take the square root of both sides:

    x - 1 = ±√ (7/2)

    6. Write out the two roots:

    x = 1 + √ (7/2) and

    x = 1 - √ (7/2)

    To the nearest hundredth:

    x = 2.87 and - 0.87
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