The question is...
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?
Answer:
3.122
Step-by-step explanation:
49x^2+56x-64 = 0
49(x^2+56x/49) - 64 = 0
49(x^2+8x/7) = 60
introduce a new constant to form (ax+b)^2 form from the multiplier of x
New constant = ((8/7) ÷ 2)^2
= (8/14)^2
Put the constant into equation plus another equal constant with negative value
49(x^2 + 8x/7 + (8/14)^2 - (8/14)^2) = 60
Reduce the following part
x^2 + 8x/7 + (8/14)^2 = (x + 8/14)^2
Put back into equation:
49((x + 8/14)^2) - 49(8/14)^2 = 60
49((x + 8/14)^2) = 60 + 49(8/14)^2
= 60 + 49(64/196)
= 60 + 16 = 76
(x + 8/14)^2 = 76/49
Equating with (ax + b)^2 = c
a = 1, b = 8/14, c = 76/49
a + b + c = 1 + 8/14 + 76/49 = 3.122
