? asked in 科學及數學數學 · 1 decade ago

Completing the square?

What do people mean when they say "complete the square to solve a quadratic equation"?

ie. 3t^2+4t-2=0

solve it by completing the square.

Update:

note that not all quadratic equation can be solved by cross method.

Update 2:

Please write formulas for it please. Not only how to solve the ie question, but how to solve generally speaking.

2 Answers

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  • 1 decade ago
    Favorite Answer

    3t^2 + 4t - 2 = 0

    3(t^2 + 4/3 t) - 2 = 0

    (t^2 + 4/3 t) - 2/3 = 0

    (t + 4/3 t + 4/9) - 4/9 - 2/3 = 0

    (t + 2/3)^2 - 10/9 = 0 ... thus completing the square

    (t + 2/3)^2 = 10/9

    t + 2/3 = sqrt10 / 3 or -sqrt10 / 3

    t = (sqrt10 -2) / 3 or (- sqrt10 - 2) / 3

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  • 1 decade ago

    3t^2+4t-2

    =3(t^2+4/3)-2

    =3(t+2/3)^2-2

    * I JUST KNOW HOW TO WRITE IN THE FORM OF COMPLETING THE SQUARE. IF YOU WANT TO FIND THE VALUE OF t, CROSS METHOD IS MORE SUITABLE!!

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