A student was given the equation x^2+2x-16=0 to solve by completing the square. The first step that was written is shown below.

Question

A student was given the equation x^2+2x-16=0 to solve by completing the square. The first step that was written is shown below. ——> X^2 + 2x=16<—— The next step in the student’s process was x^2 +2x+c =16+c. State the value of c that creates a perfect square trinomial.

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Elliana 1 month 2021-10-20T14:08:14+00:00 1 Answer 0 views 0

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    2021-10-20T14:09:47+00:00

    Answer:

    x_{1}=-1+\sqrt{17},\:x_{2}=-1-\sqrt{17}

    Step-by-step explanation:

    Quadratic Equation Given:

    x^2+2x-16=0

    x^2 + 2x=16

    $c=\left( \frac{b}{2} \right)^2 $

    x^2 + 2x+1=16+1

    (x+1)^2=17\\

    x+1=\pm \sqrt{17} \\

    x=-1 \pm \sqrt{17} \\

    x_{1}=-1+\sqrt{17},\:x_{2}=-1-\sqrt{17}

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