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# Algebra

0
35
1

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
+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