Final answer:
To solve the equation with rational exponents, isolate the variable x by simplifying the expression (ˣ²-x-9)⁹³/⁴ to √(ˣ²-x-9)³. Then, move the constants to the other side of the equation and simplefy. Finally, solve for x using factoring, completing the square, or the quadratic formula.
Step-by-step explanation:
To solve the equation with rational exponents, we need to isolate the variable x. Let's begin by simplifying the rational exponent expression. The expression (ˣ²-x-9)⁹³/⁴ can be written as √(ˣ²-x-9)³. Now, let's isolate the variable by moving the constants to the other side of the equation. Subtracting 14 from both sides gives us √(ˣ²-x-9)³ = 27. Cube both sides to eliminate the radical and we get ˣ²-x-9 = 27³ = 19683. This is now a quadratic equation. Rearranging the terms, we have ˣ² - x - 19692 = 0. To solve for x, we can use factoring, completing the square, or the quadratic formula.