Factor x^2+9x+81/4

Problem

x^2+9*x+81/4

Solution

1. Identify the structure of the expression as a potential perfect square trinomial of the form a^2+2*a*b+b^2

2. Determine the square root of the first term x^2 which is x

3. Determine the square root of the constant term 81/4 which is 9/2

4. Verify the middle term by calculating 2*a*b which is 2⋅x⋅9/2=9*x

5. Apply the perfect square formula (a+b)^2 using a=x and b=9/2

Final Answer

x^2+9*x+81/4=(x+9/2)^2

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