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

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


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

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

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

Reorder the terms:
(kx2 + 1x2) + -2(k + -1) * x + 1 = 0
(kx2 + 1x2) + -2(k + -1) * x + 1 = 0

Reorder the terms:
kx2 + 1x2 + -2(-1 + k) * x + 1 = 0

Reorder the terms for easier multiplication:
kx2 + 1x2 + -2x(-1 + k) + 1 = 0
kx2 + 1x2 + (-1 * -2x + k * -2x) + 1 = 0

Reorder the terms:
kx2 + 1x2 + (-2kx + 2x) + 1 = 0
kx2 + 1x2 + (-2kx + 2x) + 1 = 0

Reorder the terms:
1 + -2kx + kx2 + 2x + 1x2 = 0

Solving
1 + -2kx + kx2 + 2x + 1x2 = 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 + kx2 + 2x + -1 + 1x2 = 0 + -1

Reorder the terms:
1 + -1 + -2kx + kx2 + 2x + 1x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2kx + kx2 + 2x + 1x2 = 0 + -1
-2kx + kx2 + 2x + 1x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2kx + kx2 + 2x + 1x2 = -1

Add '-2x' to each side of the equation.
-2kx + kx2 + 2x + -2x + 1x2 = -1 + -2x

Combine like terms: 2x + -2x = 0
-2kx + kx2 + 0 + 1x2 = -1 + -2x
-2kx + kx2 + 1x2 = -1 + -2x

Add '-1x2' to each side of the equation.
-2kx + kx2 + 1x2 + -1x2 = -1 + -2x + -1x2

Combine like terms: 1x2 + -1x2 = 0
-2kx + kx2 + 0 = -1 + -2x + -1x2
-2kx + kx2 = -1 + -2x + -1x2

Reorder the terms:
1 + -2kx + kx2 + 2x + x2 = -1 + -2x + -1x2 + 1 + 2x + x2

Reorder the terms:
1 + -2kx + kx2 + 2x + x2 = -1 + 1 + -2x + 2x + -1x2 + x2

Combine like terms: -1 + 1 = 0
1 + -2kx + kx2 + 2x + x2 = 0 + -2x + 2x + -1x2 + x2
1 + -2kx + kx2 + 2x + x2 = -2x + 2x + -1x2 + x2

Combine like terms: -2x + 2x = 0
1 + -2kx + kx2 + 2x + x2 = 0 + -1x2 + x2
1 + -2kx + kx2 + 2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1 + -2kx + kx2 + 2x + x2 = 0

The solution to this equation could not be determined.

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