The square of a binomial expands as follows:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Expanding all the binomials, we have
[tex]4k^2-36k+81+k^2+4k+4=4k^2+4k+1+k^2-16k+64[/tex]
Sum like terms:
[tex]5k^2-32k+85=5k^2-12k+65[/tex]
Simplify terms appearing on both sides:
[tex]-32k+85=-12k+65[/tex]
Move all terms involving k to the left and all numbers to the right:
[tex]-20k=-20[/tex]
Divide both sides by -20:
[tex]k=1[/tex]
