Po is trying to solve the following equation by completing the square: 49x^2+56x-64 = 0. He successfully rewrites the above equation in the following form: (ax + b) ^2 = c, where a, b, and c are integers and a > 0. What is the value of a + b + c?

Halp

(ax+b) ² = c

(ax+b) (ax+b) = c

(ax+b) (ax+b) = a²x² + abx + abx + b²

a²x² + 2abx + b² - c = 0

49x² + 56x - 64 = 0

a² = 49

a = 7 or - 7

* given that a > 0; so a = 7

2ab = 56

ab = 56/2

ab = 28

b = 28/a

b = 4

- 64 = b² - c

- 64 = 16 - c

- 64 - 16 = - c

-80 = - c

80 = c

(7x + 4) ² = 80

Check = (7x+4) (7x+4) - 80 = 0

49x² + 28x + 28x + 16 - 80 = 0

49x² + 56x + 64 = 0

Then; a + b + c

7 + 4 + 80 = 91