Factor x^2+5x+25/4

Problem

x^2+5*x+25/4

Solution

1. Identify the structure of the quadratic 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, 25/4 which is 5/2

4. Verify the middle term by calculating 2*a*b which is 2⋅x⋅5/2=5*x

5. Apply the formula for a perfect square trinomial, a^2+2*a*b+b^2=(a+b)^2 using a=x and b=5/2

Final Answer

x^2+5*x+25/4=(x+5/2)^2

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