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

`x_(1)=-1+√(17),\:x_(2)=-1-√(17)`

Explanation:

Quadratic Equation Given:

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

`x^2 + 2x=16`

`$c=\left( (b)/(2) \right)^2 $`

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

`(x+1)^2=17\\`

`x+1=\pm √(17) \\`

`x=-1 \pm √(17) \\`

`x_(1)=-1+√(17),\:x_(2)=-1-√(17)`