Let's convert the word descriptions into mathematical equations first for illustration.
f(x) = x^2 - x - 12
g(x) = -2.5x - 2
Then, we equate g(x) and f(x). The final equation becomes
x^2 - x - 12 = -2.5x - 2
Then, we simplify by transposing and combining like terms.
x^2 - x + 2.5x -12 + 2 = 0
x^2 + 1.5x - 10 = 0
Since this is a quadratic equation, we find the roots by using the quadratic formula
[tex]x=[-b \ +/- \sqrt{ b^{2} -4ac}]/2a [/tex]
where a = 1, b = 1.5 and c=-10
[tex]x=[-1.5 \ + \sqrt{ 1.5^{2} -4(1)(-10)} ]/2(1)=2.5
[/tex]
[tex]x=[-1.5 \ - \sqrt{ 1.5^{2} -4(1)(-10)} ]/2(1)=-4[/tex]
Thus, the answer is x = 2.5, -4.
