To solve the equation x^2 + 25x - 10974 = 0, you can use factoring or the quadratic formula. Factoring may not be straightforward in this case, so let's use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Using the coefficients from the equation, -b would be -25, a would be 1, and c would be -10974. Substituting these values into the formula will give you two possible solutions for x.