Question

Simply (2k-9)^2+(k+2)^2=(2k+1)^2+(k-8)^2

Answer 1

The square of a binomial expands as follows:

$(a+b)^2=a^2+2ab+b^2$

Expanding all the binomials, we have

$4k^2-36k+81+k^2+4k+4=4k^2+4k+1+k^2-16k+64$

Sum like terms:

$5k^2-32k+85=5k^2-12k+65$

Simplify terms appearing on both sides:

$-32k+85=-12k+65$

Move all terms involving k to the left and all numbers to the right:

$-20k=-20$

Divide both sides by -20:

$k=1$