Question 983024

the discriminant must be equal to {{{0}}} for perfect square polynomials

so, add a variable for the constant {{{k}}}, then get a formula for the discriminant {{{(b^2 - 4ac)}}}, then determine the value of {{{k}}} to make it {{{0}}}

{{{x^2+(5/6)x+k}}}

{{{(b^2 - 4ac)= 0}}}

{{{((5/6)^2 - 4*1*k)=0}}}

{{{25/36- 4k=0}}}

{{{25/36=4k}}}

{{{(25/36)/4=k}}}

{{{k=25/144 }}}

{{{x^2+(5/6)x+25/144}}}

{{{(x^2+25/144)^2}}}


or simple, take half of the x-coefficient {{{(5/6)}}} to get {{{(5/12)}}}, then

square {{{(5/12)}}} to get {{{(25/144)}}} and that is your constant {{{k}}}

you need to add   

{{{x^2+(5/6)x+k}}}

{{{x^2+(5/6)x+25/144}}}

{{{(x^2+25/144)^2}}}