Patricia is trying to solve the following equation by completing the square:
25x^2 + 40x - 10 = 0
She 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?
+592 \(25x^2 + 40x - 10 = 0\)
\(25x^2 + 40x + (\frac{40\div2}{5})^2 - (\frac{40\div2}{5})^2 - 10 = 0\)
\(25x^2 + 40x + 16 - 16 - 10 = 0\)
\((5x + 4)^2 - 16 - 10 = 0 \)
\((5x + 4)^2 = 26\)
therefore the value of a + b + c is 5 + 4 + 26, which equals 35.
