Question

To show how to solve the equation, create two functions and find their intersection points. What two functions can be used to solve the following equation, and what is their solution set?

10 - x^2 = x + 4

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

Two functions that can be used to solve the equation are:

f(x) = 10 - x^2
g(x) = x + 4

To find the intersection points of these two functions, we can set them equal to each other:

10 - x^2 = x + 4

Rearranging the equation, we get:

x^2 + x - 6 = 0

Now, we can solve for x by factoring or using the quadratic formula. Factoring gives:

(x + 3)(x - 2) = 0

Setting each factor equal to zero gives the solutions:

x + 3 = 0 --> x = -3
x - 2 = 0 --> x = 2

So, the solution set for the equation is {x = -3, x = 2}.