algebra

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Solve the quadratic equation by completing the square.
-3x^2+9x=1

Not sure how to do these, if someone could expplain.

  • algebra -

    it's usually easier to have a positive coefficient for x^2, so let's take care of that first:

    3x^2 - 9x = -1
    x^2 - 3x = -1/3

    since (x-a)^2 = x^2 - 2a + a^2, you want to take half of 3 and square it, then add that to both sides:

    x^2 - 3x + 9/4 = -1/3 + 9/4

    Now you have a perfect square on the left:

    (x-3/2)^2 = 23/12

    now take square roots:

    x - 3/2 = ±√(23/12) = ±√69/6

    so,

    x = 3/2 ±√69/6
    or,
    x = (9±√69)/6

    Note how that is the solution using the quadratic formula.

  • algebra -

    Still confused, but I'll try another one and see if I get it. Thank you.

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