Po is trying to solve the following equation by completing the square49x^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 ?

tertre
Mar 11, 2017

#1**0 **

49x^2+56x-64 = 0

49x^2 + 56x = 64 divide through by 49

x^2 + (56/49)x = 64/49

x^2 + (8/7)x = 64/49

Take (1/2) of (8/7) = 8/14 = 4/7 square it = 16/49 add to both sides

x^2 + (8/7)x + 16/49 = 64/49 + 16/49

x^2 + (8/7)x + 16/49 = 80/49 multiply through by 49

49x^2 + 56x + 16 = 80 factor the left side

(7x + 4)^2 = 80

a = 7, b = 4 , c = 8

a + b + c = 19

CPhill
Mar 11, 2017