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 $a + b + c$?
One way to do this is to expand the second equation and compare the coefficients of each term with the first equation. Expanding the second equation, I get $$a^2x^2 + 2abx + b^2 = c.$$ Comparing the coefficients of $x^2$, I see that $a^2 = 49$, so $a = \sqrt{49} = 7$. Comparing the coefficients of $x$, I see that $2ab = 56$, so $ab = 28$. Since I know that $a = 7$, I can divide both sides by $7$ to get $b = 4$. Now I have the values of $a$, $b$, and $c$, so I can add them up to get the answer. The value of $a + b + c$ is $7 + 4 + 80 = 91$. 