Minervino Zabel

To help understand, let's make up a simple problem. (x-1)x = 1/2(x-1). If you divide by (x-1) on both sides to solve, the answer is x = 1/2. But let's multiply it out and solve a different way.

(x-1)x = 1/2(x-1)

x2 - x = 1/2x - 1/2

2(x2 - x) = 2(1/2x - 1/2)

2x2 - 2x = x - 1

2x2 - 3x + 1 = 0

(2x - 1)(x - 1) = 0

(2x - 1) = 0 or (x - 1) = 0

x = 1/2 or x = 1

Plugging those numbers in, we see that both are truly correct answers.

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