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7 September, 03:48

A^2-a+12=0 I need the roots

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  1. 7 September, 07:00
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    a = 1/2 (1 ±sqrt (47))

    Step-by-step explanation:

    a^2-a+12=0

    We will complete the square

    Subtract 12 from each side

    a^2-a+12-12=0-12

    a^2-a=-12

    The coefficient of a = - 1

    -Divide by 2 and then square it

    (-1/2) ^2 = 1/4

    Add it to each side

    a^2 - a + 1/4=-12 + 1/4

    (a-1/2) ^2 = - 11 3/4

    (a-1/2) ^2 = - 47/4

    Take the square root of each side

    sqrt ((a-1/2) ^2) = sqrt (-47/4)

    a-1/2 = ±i sqrt (1/4) sqrt (47)

    a-1/2 = ±i/2 sqrt (47)

    Add 1/2 to each side

    a-1/2+1/2 = 1/2± i/2 sqrt (47)

    a = 1/2± i/2 sqrt (47)

    a = 1/2 (1 ±sqrt (47))
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