Final answer:
The student's equation, once simplified, is a polynomial equation that is not in quadratic form and cannot be directly solved using the quadratic formula. It may require different algebraic methods or numerical approaches to find solutions.
Step-by-step explanation:
The student is asked to solve the equation by first simplifying and then using techniques for solving quadratic equations. Upon simplifying, the equation (8x² + 13 + 2x² – 12x⁴ + 11 - 11 - 6x) = (-2x² - 1) becomes -10x⁴ + 10x² - 6x + 12 = 0. Regrouping, this can be written as (-10x⁴ - 6x + 10x² + 12), which is a polynomial equation, not a simple quadratic, and cannot be directly solved using the quadratic formula. It would need different algebraic techniques like factoring, completing the square, or numerical methods to find approximate solutions if they exist.
Regarding the other equations provided in the reference, it's clear they demonstrate how to handle equations of the quadratic form ax² + bx + c = 0, including the use of the quadratic formula and understanding the multiplication rules for signs. However, these references are for different equations than the one asked about by the student and thus are not directly applicable to their equation.