7n^2-4n-14=21

complete the square

Answer: (7n - 2) ² = 249

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.