2x^2-(k-1)(k-1)x+k-2=0

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Solution for 2x^2-(k-1)(k-1)x+k-2=0 equation: 


Simplifying
2x2 + -1(k + -1)(k + -1) * x + k + -2 = 0

Reorder the terms:
2x2 + -1(-1 + k)(k + -1) * x + k + -2 = 0

Reorder the terms:
2x2 + -1(-1 + k)(-1 + k) * x + k + -2 = 0

Reorder the terms for easier multiplication:
2x2 + -1x(-1 + k)(-1 + k) + k + -2 = 0

Multiply (-1 + k) * (-1 + k)
2x2 + -1x(-1(-1 + k) + k(-1 + k)) + k + -2 = 0
2x2 + -1x((-1 * -1 + k * -1) + k(-1 + k)) + k + -2 = 0
2x2 + -1x((1 + -1k) + k(-1 + k)) + k + -2 = 0
2x2 + -1x(1 + -1k + (-1 * k + k * k)) + k + -2 = 0
2x2 + -1x(1 + -1k + (-1k + k2)) + k + -2 = 0

Combine like terms: -1k + -1k = -2k
2x2 + -1x(1 + -2k + k2) + k + -2 = 0
2x2 + (1 * -1x + -2k * -1x + k2 * -1x) + k + -2 = 0

Reorder the terms:
2x2 + (2kx + -1k2x + -1x) + k + -2 = 0
2x2 + (2kx + -1k2x + -1x) + k + -2 = 0

Reorder the terms:
-2 + k + 2kx + -1k2x + -1x + 2x2 = 0

Solving
-2 + k + 2kx + -1k2x + -1x + 2x2 = 0

Solving for variable 'k'.

The solution to this equation could not be determined.

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