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Algebra Quadratic Equations

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I am trying to define the different appraoches to solving quadratic equations. My book says using quadratic formula, completing the sqaure and factoring.

I thought completing the square would be by facotring? How are these two different?

  • Algebra Quadratic Equations - ,

    Completing the square is a variation, I suppose, of factoring. The idea is to make the number, which isn't factorable (is that a word?) into one that can be factored. For example,
    X^2 + 4x + 4 can be factored into (x+2)^2. So if we had an equation, such as
    X^2 + 4x + 3, we rearrange the equation to
    X^2 + 4x + ..... = -3
    Then we add 4 to both sides, like this,
    X^2 + 4x + 4 = -3 + 4
    Now the left side is a perfect square
    (X + 2)^2 = +1
    and we solve for X.
    I hope this answers your question.

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