Final answer:
Complex quadratic equations can be simplified and solved using various methods like the quadratic formula, recognizing perfect squares, or completing the square.
Step-by-step explanation:
The student has presented an equation that at first glance might appear complex but can be addressed by identifying it as a quadratic equation and using appropriate methods to solve it. When working with quadratic equations, such as x² + 25 = 100 - 2x, we can move all terms to one side to set the equation equal to 0 and then solve for the unknown value of x.
This might involve using the quadratic formula or factoring, depending on the form of the equation. Often, it helps to simplify the expression and look for any patterns that might indicate a perfect square to make the process easier.
To find the sum of the solutions of the equation, we can use the formula -b/a from the quadratic equation ax² + bx + c = 0, where a, b, and c are coefficients and x represents the unknown value we're solving for.