Answer:
There is some mistake in the question, because the solutions are x = -1.445 and x = -34.555
Step-by-step explanation:
Given the functions:
f(x) = x² + 4x + 10
g(x) = -32x - 40
we want to find the points at which f(x) = g(x).
x² + 4x + 10 = -32x - 40
x² + 4x + 10 + 32x + 40 = 0
x² + 36x + 50 = 0
Using quadratic formula:
[tex]x = \frac{-b \pm \sqrt{b^2-4(a)(c)}}{2(a)} [/tex]
[tex]x = \frac{-36 \pm \sqrt{36^2-4(1)(50)}}{2(1)} [/tex]
[tex]x = \frac{-36 \pm 33.11}{2} [/tex]
[tex]x_1 = \frac{-36 + 33.11}{2} [/tex]
[tex]x_1 = -1.445 [/tex]
[tex]x_2 = \frac{-36 - 33.11}{2} [/tex]
[tex]x_2 = -34.555[/tex]
