Question 133599
Step 1: Divide the entire polynomial by the coefficient on the {{{x^2}}} term.  {{{x^2+3x+k/4}}}


Step 2: Divide the coefficient on the {{{x}}} term by 2:  Result: {{{3/2}}}


Step 3: Square the result of step 2:  Result: {{{9/4}}}


The result of step 3 is the value of the constant term required to make {{{x^2+3x+k/4}}} a perfect square, therefore {{{k/4=9/4}}} => {{{k=9}}}


{{{x^2+3x+9/4}}} can be multiplied by 4 to reverse the effects of step 1, resulting in {{{4x^2+12x+9}}} which then factors to {{{(2x+3)(2x+3)=(2x+3)^2}}}