Final answer:
Solving the equation u + 6² = 2u² + 9u + 26 involves simplifying and rearranging the equation into a quadratic form and then using the quadratic formula, factoring, or completing the square to find the value(s) of u.
Step-by-step explanation:
To solve for u in the equation u + 6² = 2u² + 9u + 26, we first need to simplify and rearrange the equation into standard quadratic form. Start by simplifying 6² to 36. Then, subtract u and 36 from both sides to get the equation into 0 = 2u² + 8u - 10. Now, you can solve the quadratic equation using the quadratic formula, factoring, or completing the square method. For the quadratic formula, the solutions for u are given by u = [-b ± √(b² - 4ac)] / (2a), where a = 2, b = 8, and c = -10.