Answer:
q = 10
Explanation:
The desired form is a rearrangement of the given equation, divided by the leading coefficient.
Monic polynomial
A monic polynomial is one with a leading coefficient of 1. The desired form requires that we start from that condition. In order to avoid fractions, we can begin by subtracting the constant term on the left.
2x^2 -20x +49 = 19 . . . . . . given
2x^2 -20x = -30 . . . . . . . . subtract 49
x^2 -10x = -15 . . . . . . . . . divide by 2
Completing the square
The square of the binomial a+b is given by ...
(x +b)^2 = x^2 +2bx +b^2
That is the constant term on the right is the square of half the coefficient of x. To achieve this perfect square trinomial in our equation, we need to add the square of half of -10.
x^2 -10x +25 = -15 +25 . . . . . . add (-10/2)^2 = 25 to both sides
(x -5)^2 = 10 . . . . . . . . . . . write in the desired form
The value of q in the form ...
(x -p)^2 = q
is 10.