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
Two functions that can be used to solve the equation 10−x^2=x+4 are:
1. f(x) = 10−x^2
2. g(x) = x+4
Their intersection points are the solutions to the equation.
To find the solution set, we need to find the points where f(x) = g(x). This means that we want to find where 10−x^2 = x+4.
Setting the two functions equal to each other:
10−x^2 = x+4
Rearranging the equation:
-x^2 - x + 6 = 0
Multiplying by -1 to make it easier to solve:
x^2 + x - 6 = 0
Factoring the equation:
(x+3)(x-2) = 0
So, x = -3 or x = 2
Therefore, the solution set to the equation 10−x^2=x+4 is:
{x = -3, x = 2}