Question

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

Answer 1

(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