(x+4)x^4+4x^3+kx^2+4x+1=0

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Solution for (x+4)x^4+4x^3+kx^2+4x+1=0 equation:


Simplifying
(x + 4) * x4 + 4x3 + kx2 + 4x + 1 = 0

Reorder the terms:
(4 + x) * x4 + 4x3 + kx2 + 4x + 1 = 0

Reorder the terms for easier multiplication:
x4(4 + x) + 4x3 + kx2 + 4x + 1 = 0
(4 * x4 + x * x4) + 4x3 + kx2 + 4x + 1 = 0
(4x4 + x5) + 4x3 + kx2 + 4x + 1 = 0

Reorder the terms:
1 + kx2 + 4x + 4x3 + 4x4 + x5 = 0

Solving
1 + kx2 + 4x + 4x3 + 4x4 + x5 = 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 + kx2 + 4x + 4x3 + 4x4 + -1 + x5 = 0 + -1

Reorder the terms:
1 + -1 + kx2 + 4x + 4x3 + 4x4 + x5 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + kx2 + 4x + 4x3 + 4x4 + x5 = 0 + -1
kx2 + 4x + 4x3 + 4x4 + x5 = 0 + -1

Combine like terms: 0 + -1 = -1
kx2 + 4x + 4x3 + 4x4 + x5 = -1

Add '-4x' to each side of the equation.
kx2 + 4x + 4x3 + 4x4 + -4x + x5 = -1 + -4x

Reorder the terms:
kx2 + 4x + -4x + 4x3 + 4x4 + x5 = -1 + -4x

Combine like terms: 4x + -4x = 0
kx2 + 0 + 4x3 + 4x4 + x5 = -1 + -4x
kx2 + 4x3 + 4x4 + x5 = -1 + -4x

Add '-4x3' to each side of the equation.
kx2 + 4x3 + 4x4 + -4x3 + x5 = -1 + -4x + -4x3

Reorder the terms:
kx2 + 4x3 + -4x3 + 4x4 + x5 = -1 + -4x + -4x3

Combine like terms: 4x3 + -4x3 = 0
kx2 + 0 + 4x4 + x5 = -1 + -4x + -4x3
kx2 + 4x4 + x5 = -1 + -4x + -4x3

Add '-4x4' to each side of the equation.
kx2 + 4x4 + -4x4 + x5 = -1 + -4x + -4x3 + -4x4

Combine like terms: 4x4 + -4x4 = 0
kx2 + 0 + x5 = -1 + -4x + -4x3 + -4x4
kx2 + x5 = -1 + -4x + -4x3 + -4x4

Add '-1x5' to each side of the equation.
kx2 + x5 + -1x5 = -1 + -4x + -4x3 + -4x4 + -1x5

Combine like terms: x5 + -1x5 = 0
kx2 + 0 = -1 + -4x + -4x3 + -4x4 + -1x5
kx2 = -1 + -4x + -4x3 + -4x4 + -1x5

Divide each side by 'x2'.
k = -1x-2 + -4x-1 + -4x + -4x2 + -1x3

Simplifying
k = -1x-2 + -4x-1 + -4x + -4x2 + -1x3

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