If (x/100-1) (x/100+1) = kx^2-1 k=

(x/100-1) (x/100+1) = kx^2-1

(x/100-1) (x/100+1) = (x/100) ^2 - 1^2 because it's a difference of squares ((a-b) (a+b) = a^2-ab+ab-b^2 = a^2 - b^2):

(x/100) ^2 - 1^2=kx^2 - 1

(x/100) ^2 - 1=kx^2 - 1

(x/100) ^2=kx^2

(x^2) / (100^2) = kx^2

1 / (100^2) = k

1/10000=k

k=0.0001