answer: n = -5 or 9
steps:
100 + (n - 2)² = 149
step 1: expand
100 + n² - 4n + 4 = 149
100 + n² - 4n + 4 = 149step 2: rearrange
100 + n² - 4n + 4 = 149step 2: rearrangen² - 4n + 100 + 4 - 149 = 0
100 + n² - 4n + 4 = 149step 2: rearrangen² - 4n + 100 + 4 - 149 = 0n² - 4n - 45 = 0
step 3: simplify
n² - 4n - 45 = 0
(n + 5) (n - 9) = 0
step 4: answer
n + 5 = 0 or n - 9 = 0
n = -5 or n = 9