To solve the quadratic equation \( x^2 + 7x + 10 = 0 \), we can factor it. We are looking for two numbers that multiply to \( 10 \) (the constant term) and add up to \( 7 \) (the coefficient of the \( x \) term).
The numbers that meet these criteria are \( 2 \) and \( 5 \). Thus, we can factor the equation as follows:
\[ (x + 2)(x + 5) = 0 \]
Setting each factor equal to zero gives us:
- \( x + 2 = 0 \) → \( x = -2 \)
- \( x + 5 = 0 \) → \( x = -5 \)
Therefore, the solutions to the equation \( x^2 + 7x + 10 = 0 \) are:
\[ x = -2 \quad \text{or} \quad x = -5 \]
The correct answer is A. X = -2 or x = -5.