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26 January, 14:38

How can I isolate x in y=6x-2x²

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  1. 26 January, 16:35
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    x = 3/2 ± √ (9/4 - 1/2 y)

    Step-by-step explanation:

    y = 6x - 2x²

    First, factor out the leading coefficient:

    y = - 2 (x² - 3x)

    Complete the square.

    y = - 2 (x² - 3x + 9/4 - 9/4)

    y = - 2 (x² - 3x + 9/4) + 9/2

    y = - 2 (x - 3/2) ² + 9/2

    Solve for x.

    -1/2 y = (x - 3/2) ² - 9/4

    9/4 - 1/2 y = (x - 3/2) ²

    ±√ (9/4 - 1/2 y) = x - 3/2

    x = 3/2 ± √ (9/4 - 1/2 y)
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