Final answer:
The equation x^5 = -0.92 is solved by finding the fifth root of -0.92, which is approximately -0.9797. This is the principal real root, providing the solution to the equation.
Step-by-step explanation:
To solve the equation x^5 = -0.92, we need to find the fifth root of -0.92. In algebra, a fifth root of a number is a value that, when multiplied by itself five times, gives the original number. Since the equation is not quadratic and does not fit the structure ax^2 + bx + c = 0, we cannot use the quadratic formula directly. For real numbers, we can only extract even roots (like square roots or fourth roots) from positive numbers because multiplying an even number of negative factors gives a positive result. However, odd roots, such as a fifth root, can be extracted from negative numbers.
A calculator or computer software can be used to find that the fifth root of -0.92 is approximately -0.9797. This is the principal real root of the equation, which is the single real solution.