X^2 + 18x + c = 25 + c

Rearrange to: x^2 + 18x - 25 = 0

Then factorise (I like to do it by completing the square):

(x + 9) ^2 - 81 - 25 = 0

(x + 9) ^2 = 106

x + 9 = sqrt (106)

The sol'ns are:

x = - 9 + and - sqrt (106)