A student was given the equation 2x^2+ 3x +7=0 to solve by completing the square. The first step that was written is shown below.
2x² + 3x=-7
The next step in the student's process was x² + x +c= - +c State the value of c that creates a
perfect square trinomial. Explain how the value of c is determined.

where is the picture

step-by-step explanation:

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0