Solve the quadratic equation by completing the square. 6×2 + 4x – 5 = 0

Question

Solve the quadratic equation by completing the square. 6×2 + 4x – 5 = 0

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Allison 2 days 2021-09-13T03:05:34+00:00 1 Answer 0

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    2021-09-13T03:07:10+00:00

    Answer:

    $x_{1}=-\frac{2+\sqrt{34}}{6}$

    $x_{2}=-\frac{2-\sqrt{34}}{6}$

    Step-by-step explanation:

    Quadratic Equation given:

    6x^2 + 4x - 5 = 0

    Start dividing both sides by 6.

    $\frac{6}{6} x^2 +\frac{4}{6} x - \frac{5}{6}  = \frac{0}{6} $

    $x^2 +\frac{2}{3} x - \frac{5}{6}  = 0 $

    $x^2 +\frac{2}{3} x = \frac{5}{6} $

    Once, $\left( \frac{2}{3} \cdot \frac{1}{2} \right)^2=\frac{1}{9} $

    $x^2 +\frac{2}{3} x+\frac{1}{9}  = \frac{5}{6}+\frac{1}{9}  $

    $\left(x+\frac{1}{3} \right)^2 = \frac{17}{18}}  $

    $x+\frac{1}{3}  =\pm\sqrt{\frac{17}{18}} }   $

    Solving $\sqrt{\frac{17}{18}} $

    $\sqrt{\frac{17(18)}{18(18)}}= \sqrt{\frac{306}{324}}=\frac{3\sqrt{34} }{18} =\frac{\sqrt{34} }{6} $

    Then,

    $x+\frac{1}{3}  =\pm\frac{\sqrt{34} }{6}  $

    $x =-\frac{1}{3} \pm\frac{\sqrt{34} }{6}  $

    $x_{1}=-\frac{2+\sqrt{34}}{6}$

    $x_{2}=-\frac{2-\sqrt{34}}{6}$

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