Find the Perfect Square Trinomial x^2+6x

Problem

x^2+6*x

Solution

1. Identify the coefficient of the linear term x which is b=6

2. Divide the coefficient b by 2 to find the value needed for the binomial square: 6/2=3

3. Square this result to find the constant term required to complete the square: 3^2=9

4. Add the constant term to the original expression to form the perfect square trinomial: x^2+6*x+9

5. Verify that the trinomial can be written as a square of a binomial: (x+3)^2

Final Answer

x^2+6*x+9=(x+3)^2

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