Problem 14

Explanation

Given the function $g(x) = 3x + 2$. We will substitute this function into the given equation.

First, determine the forms of $g^2(x)$ and $g(x^2)$:

Substitute these forms into the initial equation:

Group like terms:

This quadratic equation has roots $x_1$ and $x_2$. The sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is $x_1 + x_2 = -\frac{b}{a}$.

Thus, the value of $x_1 + x_2$ is $-\frac{3}{5}$.