Final answer:
To solve the equation x⁻⁶ + 3x⁻³ - 14, we can substitute a = 1/x. Then, solve the resulting equation a⁶ + 3a³ - 14 using factoring or the quadratic formula.
Step-by-step explanation:
To determine the solution to the equation x⁻⁶ + 3x⁻³ - 14, we need to apply substitution. Let's let a = 1/x. So the equation becomes a⁶ + 3a³ - 14. Now we can solve this equation using factoring or the quadratic formula. Let's use factoring: (a³ + 7)(a³ - 2) = 0. Setting each factor equal to zero, we get two possible values for a: a = -7 or a = ∛2.