Factor x^2+3x+9/4

Problem

x^2+3*x+9/4

Solution

1. Identify the expression as a quadratic trinomial of the form a*x^2+b*x+c where a=1 b=3 and c=9/4

2. Check for a perfect square trinomial pattern, which follows the form a^2+2*a*b+b^2=(a+b)^2

3. Verify the terms by noting that the first term is x^2 and the last term is (3/2)^2

4. Confirm the middle term by calculating 2⋅x⋅3/2 which equals 3*x

5. Apply the perfect square formula to write the factored form.

Final Answer

x^2+3*x+9/4=(x+3/2)^2

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