Answer: (7n - 2)² = 249
Step-by-step explanation:
1) Given expression: 7n² - 4n - 14 = 21
2) Transpose - 14 =>
7n² - 4n = 21 + 14
3) Combine like terms =>
7n² - 4n = 35
4) multiply both terms by 7 =>
(7n)² - 4(7n) = 35×7
5) form the squared binomial:
(7n - 2)² - 4 = 35×7
6) Transpose - 4 =>
(7n - 2)² = 35×7 + 4
7) Do the operations on the right side:
(7n - 2)² = 249 or (7n - 2)² - 249 = 0
8) Verify the equivalence by expanding the binomial:
(7n)² - 2(7n) + 4 - 249 = 0
(7n)² - 14n - 245 = 0
Divide by 7: 7n² - 2n - 35 = 0 or 7n² - 2n = 35, which is equivalent to the given expression.