Final answer:
The original equation presented seems to have typos and the information provided does not match the question, making it impossible to solve using the provided data and answer choices. Normally, such an equation would be solved by isolating the radical and squaring both sides, but without an accurate equation, we cannot proceed with finding a solution.
Step-by-step explanation:
The question asks for the solutions to the equation x^2 + 2x - 10 = √x + 20. To find the solutions, we must first ensure that the radical is isolated. This has already been done for us as the square root is on the right-hand side. We can then square both sides of the equation to eliminate the square root, leading to the following:
x^4 + 4x^3 - 20x^2 (squared left side) = x + 20 (squared right side). Now, we have a new quadratic equation of the form ax^2 + bx + c = 0. We would then solve this new equation using the quadratic formula or factoring, depending on how complicated the equation is after simplification.
However, the provided answer choices and the information given suggest a mis-match, and the original equation seems to have typos. The solution approaches provided also correspond to different equations, not related to the original question. Therefore, we cannot provide a definitive solution to the original equation based on the given data.