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

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


Simplifying
Kx2 + 1 + -2(k + -1) * x + x2 = 0

Reorder the terms:
x2K + 1 + -2(-1 + k) * x + x2 = 0

Reorder the terms for easier multiplication:
x2K + 1 + -2x(-1 + k) + x2 = 0
x2K + 1 + (-1 * -2x + k * -2x) + x2 = 0

Reorder the terms:
x2K + 1 + (-2kx + 2x) + x2 = 0
x2K + 1 + (-2kx + 2x) + x2 = 0

Reorder the terms:
1 + -2kx + 2x + x2 + x2K = 0

Solving
1 + -2kx + 2x + x2 + x2K = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -2kx + 2x + x2 + -1 + x2K = 0 + -1

Reorder the terms:
1 + -1 + -2kx + 2x + x2 + x2K = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2kx + 2x + x2 + x2K = 0 + -1
-2kx + 2x + x2 + x2K = 0 + -1

Combine like terms: 0 + -1 = -1
-2kx + 2x + x2 + x2K = -1

Add '-2x' to each side of the equation.
-2kx + 2x + x2 + -2x + x2K = -1 + -2x

Reorder the terms:
-2kx + 2x + -2x + x2 + x2K = -1 + -2x

Combine like terms: 2x + -2x = 0
-2kx + 0 + x2 + x2K = -1 + -2x
-2kx + x2 + x2K = -1 + -2x

Add '-1x2' to each side of the equation.
-2kx + x2 + -1x2 + x2K = -1 + -2x + -1x2

Combine like terms: x2 + -1x2 = 0
-2kx + 0 + x2K = -1 + -2x + -1x2
-2kx + x2K = -1 + -2x + -1x2

Add '-1x2K' to each side of the equation.
-2kx + x2K + -1x2K = -1 + -2x + -1x2 + -1x2K

Combine like terms: x2K + -1x2K = 0
-2kx + 0 = -1 + -2x + -1x2 + -1x2K
-2kx = -1 + -2x + -1x2 + -1x2K

Divide each side by '-2x'.
k = 0.5x-1 + 1 + 0.5x + 0.5xK

Simplifying
k = 0.5x-1 + 1 + 0.5x + 0.5xK

Reorder the terms:
k = 1 + 0.5x-1 + 0.5x + 0.5xK

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