Question 826089
A.
{{{25x^2-70x+k=0}}}

{{{(25x^2-70x)+k=0}}}  complete the square


{{{(25x^2-70x+ _ ) - _ +k=0}}} add a number in parentheses and then subtract it after parentheses

{{{(25x-70x+49)-49+k=0}}}

{{{(5x-7)^2-49+k=0}}} =>  {{{k=49}}}

so, the perfect square is {{{(5x-7)^2=0}}] which is equal to 

{{{25x^2-70 x+49}}} in expanded form


B.
{{{x^2+x+k=0}}}

{{{(x^2+x)+k=0}}}  complete the square

{{{(x^2+x+1/4)-1/4+k=0}}}

{{{(x+1/2)^2-1/4+k=0}}} =>  {{{k=1/4}}}

so, the perfect square is {{{(x+1/2)^2=0}}] which is equal to 

{{{x^2+x+1/4=0}}} in expanded form

C)

{{{81x^2+kx+36}}} or

{{{(9x)^2+kx+6^2}}}...as you can see, {{{k}}} is equal to a product of {{{2*9}}} and {{{6}}} which is {{{k=108}}}

so, 
{{{(9x)^2+108x+36=(9x+6)^2}}}


I hope you can do the last one following these examples....