Based on the graph below, what is the solution to the equation f (x) = g (x) ?

graph of function f of x equals negative x plus 2.5 and graph of function g of x equals x squared plus 2 multiplied by x minus 8

The wording of the second function may be interpreted in several differente ways. These are some:

g (x) = (x^2 + 2) (x-8)

g (x) = x^2 + 2 (x-8)

g (x) x^2 + 2x - 8

I will work with the last one, so my system of equation is:

f (x) = - x + 2.5

g (x) = x^2 + 2x - 8

f (x) = g (x) ⇒ - x + 2.5 = x^2 + 2x - 8

x^2 + 3x - 8 - x - 2.5 = 0

x^2 + 3x - 10.5 = 0

Use the quadratic formula to solve for x:

x = [ - 3 + / - √ (3^2) - 4 (1) (-10.5) ]/2

x = - 5.07 and x = 2.07