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.

Answer 1

Answer:

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

Step-by-step explanation:

Quadratic Equation Given:

$x^2+2x-16=0$

$x^2 + 2x=16$

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

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

$(x+1)^2=17$

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

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

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