Factor Quadratic D53Cf9

1. **State the problem:** Factor the quadratic expression $$x^2 + 14x + 49$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, if it can be factored into the form $$(x + m)(x + n)$$, then $$m + n = b$$ and $$mn = c$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = 14$$, and $$c = 49$$. 4. **Find two numbers that add to $$b$$ and multiply to $$c$$:** We need $$m$$ and $$n$$ such that $$m + n = 14$$ and $$mn = 49$$. 5. **Check factors of 49:** The pairs are (1, 49), (7, 7), (-1, -49), (-7, -7). Only (7, 7) add to 14. 6. **Write the factored form:** $$x^2 + 14x + 49 = (x + 7)(x + 7) = (x + 7)^2$$. 7. **Final answer:** The factored form is $$\boxed{(x + 7)^2}$$.