Final answer:
To solve the equation x^2 + 7x + 10 = 0 by factoring, find two numbers that multiply to 10 and add to 7, which are 2 and 5. Factoring the quadratic as (x + 2)(x + 5) = 0, we find the solutions x = -2 and x = -5.
Step-by-step explanation:
To solve the quadratic equation x^2 + 7x + 10 = 0 by factoring, we seek two numbers that multiply to give the constant term (10) and add up to the linear coefficient (7).
We find that 2 and 5 satisfy both conditions: (2 * 5 = 10 and 2 + 5 = 7). Therefore, we can express the quadratic as (x + 2)(x + 5) = 0.
Setting each factor equal to zero gives us the roots of the equation:
- x + 2 = 0 → x = -2
- x + 5 = 0 → x = -5
Thus, the solution to the equation x^2 + 7x + 10 = 0 is x = -2, x = -5.