Question

Why is the answer C? Plz explain

Answer 1

Set the equations each to each other and solve for x
f(x) = g(x)
x^2 - 3x = 2x+14
x^2-3x-2x-14 = 0
x^2-5x-14 = 0 .... see note below
(x-7)(x+2) = 0
x-7 = 0 or x+2 = 0
x = 7 or x = -2
The two solutions are x = 7 or x = -2

note: we technically could stop at this line and divert to another path. Instead of finding the actual solutions, we can use the discriminant formula
d = b^2 - 4ac
to find the value of d. It turns out that
d = (-5)^2 - 4(1)(-14)
d = 81
which is a positive number. So that shows we have two solutions.