Final answer:
The solutions to the equation x⁴ - 13x² + 36 = 0 are x = -3, -2, 2, and 3.
Step-by-step explanation:
This equation is in the form ax² + bx + c = 0, where a = 1, b = 0, and c = -36. To solve this equation, we can use factoring to rewrite it as (x² - 4)(x² - 9) = 0. Then, we can solve each factor separately:
Solving x² - 4 = 0, we get x = -2 or x = 2.
Solving x² - 9 = 0, we get x = -3 or x = 3.
Therefore, the solutions to the equation x⁴ - 13x² + 36 = 0 are x = -3, -2, 2, and 3.