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Math Help - Solving Quadratic Equations by Completing the Square

  1. #1
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    Red face Solving Quadratic Equations by Completing the Square

    Hello!

    I have been doing quadratic equations and I am a little uncertain about the following question from my textbook. Thank you in advance to anyone who may be able to help me!

    Solve 2x^2 + 4x - 6 = 0 by first finding a common factor and using the 'completing the square' method.
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  2. #2
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    Quote Originally Posted by JadeKiara View Post
    Hello!

    I have been doing quadratic equations and I am a little uncertain about the following question from my textbook. Thank you in advance to anyone who may be able to help me!

    Solve 2x^2 + 4x - 6 = 0 by first finding a common factor and using the 'completing the square' method.
    divide every term by 2 ...

    x^2 + 2x - 3 = 0

    x^2 + 2x = 3

    x^2 + 2x + 1 = 3 + 1

    (x+1)^2 = 4

    x+1 = \pm 2

    x = -1 \pm 2

    x = -3

    x = 1
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  3. #3
    Senior Member eumyang's Avatar
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    It's easier to complete the square if the x^2 coefficient is 1, so first factor out the 2:
    \begin{aligned}<br />
2x^2 + 4x - 6 &= 0 \\<br />
2(x^2 + 2x - 3) &= 0 \\<br />
x^2 + 2x - 3 &= 0<br />
\end{aligned}
    What I did at the last step was divide both sides by 2. Now move the constant term to the other side and complete the square:
    \begin{aligned}<br />
x^2 + 2x  &= 3 \\<br />
x^2 + 2x  + 1 &= 3 + 1 \\<br />
(x + 1)^2 &= 4 \\<br />
x + 1 &= \pm 2 \\<br />
x + 1 &= 2 \rightarrow x = 1 \\<br />
x + 1 &= -2 \rightarrow x = -3<br />
\end{aligned}

    EDIT: Ack, too slow! ^o^
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    Quote Originally Posted by JadeKiara View Post
    Hello!

    I have been doing quadratic equations and I am a little uncertain about the following question from my textbook. Thank you in advance to anyone who may be able to help me!

    Solve 2x^2 + 4x - 6 = 0 by first finding a common factor and using the 'completing the square' method.

    0=2x^2 + 4x - 6=2(x^2+2x-3)=2(x-1)(x+3)... , or also

    0=2x^2 + 4x - 6=2(x^2+2x-3)=2\left[(x+1)^2-4\right]=2(x+1-2)(x+1+2) ...

    The first method is the direct one, the trinomial decomposition. The second one uses the completion of the square method.
    Tonio
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