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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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mirai123

Answer:

[tex]x_{1}=-1+\sqrt{17},\:x_{2}=-1-\sqrt{17}[/tex]

Step-by-step explanation:

Quadratic Equation Given:

[tex]x^2+2x-16=0[/tex]

[tex]x^2 + 2x=16[/tex]

[tex]$c=\left( \frac{b}{2} \right)^2 $[/tex]

[tex]x^2 + 2x+1=16+1[/tex]

[tex](x+1)^2=17\\[/tex]

[tex]x+1=\pm \sqrt{17} \\[/tex]

[tex]x=-1 \pm \sqrt{17} \\[/tex]

[tex]x_{1}=-1+\sqrt{17},\:x_{2}=-1-\sqrt{17}[/tex]

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