Factor x^2+14x+49

Problem

x^2+14*x+49

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c where a=1 b=14 and c=49

2. Recognize that the expression is a perfect square trinomial because the first term is x^2 the last term is 7^2 and the middle term is 2⋅x⋅7

3. Apply the formula for a perfect square trinomial, a^2+2*a*b+b^2=(a+b)^2

4. Substitute a=x and b=7 into the formula to obtain the factored form.

Final Answer

x^2+14*x+49=(x+7)^2

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