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Math Help - Basic factoring question

  1. #1
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    Basic factoring question

    Hi, my factoring is not too good. How do I factor this and solve for 0?:

    x^2 + 2x + 2 = 0

    Thanks, Kim
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  2. #2
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    Quote Originally Posted by Kim Nu View Post
    Hi, my factoring is not too good. How do I factor this and solve for 0?:

    x^2 + 2x + 2 = 0

    Thanks, Kim

    Since there are not factors of 2=2\cdot 1 that add up to two. This will not factor over the Rational Numbers. We can, however, complete the square(or use the quadratic formula ) to obtain solutions and factorizations.

    First lets move the constant to the other side

    x^2+2x+2=0 \iff x^2+2x=-2

    To complete the square we take half of the b term b=2

    \frac{2}{2}=1 and then we square it to get 1^1=1.<br />

    We now add this to both sides of the equation to get

    x^2+2x+1=-1 now we can factor the left hand side to get

    (x+1)^2=-1

    Now to solve for zero we will get complex solutions because there is no Real number that when you square it you will get a negative one. To solve form here take the square root of both sides are remember that \sqrt{-1}=i with that said....

    Since you asked for a factorization we can add one to both sides to get

    (x+1)^2+1=0 we can rewrite this as

    (x+1)^2-(-1)=0 but -1=i^2 so we get

    (x+1)^2-i^2=0 this is a difference of squares so we get

    [(x+1)-i][(x+1)+i]=0

    You can solve this from here using the zero factor principle.
    Note you will get the same solutions as from above, or if you use the quadratic formula.

    I hope this helps.
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  3. #3
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    Doesn't factor

    That equation does not factor. You will need to use the quadratic formula to solve for 0.

    Go to here for more info:
    Quadratic equation - Wikipedia, the free encyclopedia

    Hope that helps.

    Now if you typed the question wrong and it's supposed to be x^2+3x+2 then it can factor to (x+2)(x+1), but the one you've typed cannot be factored.
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by AlgebraAnswers View Post
    That equation does not factor.
    Over what? The Equation does factor over the complex numbers. As I stated in my post it doesn't factor over the rationals(or the Reals). If you use the quadratic formula you will get the same solutions as I did by factoring.
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