Final answer:
Through substitution, we transform the complex expression into a standard quadratic equation by letting u = 3x + 2, resulting in u2 + 7u - 8 = 0. We can then use the quadratic formula or factoring to solve for u, and finally revert the substitution to solve for x.
Step-by-step explanation:
The student has asked how to use substitution to write an equivalent quadratic equation for the expression (3x + 2)2 + 7(3x + 2) − 8 = 0.
Frist, let's introduce a substitution variable, let's say u, where u = 3x + 2. So, our expression now looks like u2 + 7u − 8 = 0. This is a simpler quadratic equation we can work with.
Next, to find the values of x, we substitute back by replacing u with 3x + 2 after solving for u. If necessary, we could also use the quadratic formula which is u = −b ± √(b2 - 4ac) divided by 2a for the equation au2 + bu + c = 0, where a, b, and c are coefficients from the quadratic equation. In this case, a = 1, b = 7, and c = -8.