Final answer:
The quadratic equation x^2 + 5x - 9 = 0 can't be factored because there are no two real numbers that can satisfy the conditions required for factoring. Instead, the quadratic formula must be used to find the roots.
Step-by-step explanation:
The quadratic equation in question is x^2 + 5x - 9 = 0. When attempting to factor a quadratic equation, we need two numbers that multiply to give us the constant term (in this case -9) and add to give us the coefficient of the x term (in this case 5). Unfortunately, there are no two such real numbers that satisfy both conditions for this equation. Therefore, the equation is not factorable over the integers or rational numbers.
To find the roots of such an equation, one would typically use the quadratic formula, which is given by: x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the terms in the quadratic equation ax^2+bx+c = 0.