The graphs of f (x) and g (x) are shown below: graph of function f of x equals x squared minus x minus 12. Graph of function g of x equals negative 2.5 times x minus 2 What are the solutions to the equation f (x) = g (x) ? x = - 3, 4 x = - 4, 2.5 x = - 0.8, 2.5 x = 8, - 8

x = - 4, 2.5

Step-by-step explanation:

Let's write this problem algebraically

f (x) = x^2 - x - 12

g (x) = - 2.5x - 2

We want to find the solutions to the equation f (x) = g (x) so we set them equal to each other

f (x) = g (x)

x^2 - x - 12 = - 2.5x - 2

Adding 2.5x and 2 to both sides,

x^2 + 1.5x - 10 = 0

Factoring, we get

(x + 4) (x - 2.5) = 0

So,

x + 4 = 0 ⇒ x = - 4

x - 2.5 = 0 ⇒ x = 2.5