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35
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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?

 Nov 16, 2021
 #1
avatar+579 
+1

                                      \(25x^2 + 40x - 10 = 0\)
\(25x^2 + 40x + (\frac{40\div2}{5})^2 - (\frac{40\div2}{5})^2 - 10 = 0\)

                   \(25x^2 + 40x + 16 - 16 - 10 = 0\)

                                \((5x + 4)^2 - 16 - 10 = 0 \)

                                                    \((5x + 4)^2 = 26\)

 

therefore the value of a + b + c is 5 + 4 + 26, which equals 35. 

 Nov 16, 2021

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