To factor the quadratic expression \(x^2 + 14x + 49\), we can look for two numbers that multiply to 49 (the constant term) and add up to 14 (the coefficient of the \(x\) term).
The numbers 7 and 7 work because:
- \(7 \times 7 = 49\)
- \(7 + 7 = 14\)
Thus, we can factor the expression as:
\[ (x + 7)(x + 7) \quad \text{or simply} \quad (x + 7)^2 \]
So the factored form of \(x^2 + 14x + 49\) is:
\[ (x + 7)^2 \]