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Simplifying (x4) + (4x3) + (kx2) + (4x) + (1) = 0 x4 + (4x3) + (kx2) + (4x) + (1) = 0 x4 + (4x3) + kx2 + (4x) + (1) = 0 x4 + (4x3) + kx2 + (4x) + 1 = 0 Reorder the terms: 1 + kx2 + (4x) + (4x3) + x4 = 0 Solving 1 + kx2 + (4x) + (4x3) + x4 = 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) + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + kx2 + (4x) + (4x3) + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + kx2 + (4x) + (4x3) + x4 = 0 + -1 kx2 + (4x) + (4x3) + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 kx2 + (4x) + (4x3) + x4 = -1 Add '(-4x)' to each side of the equation. kx2 + (4x) + (4x3) + (-4x) + x4 = -1 + (-4x) Reorder the terms: kx2 + (4x) + (-4x) + (4x3) + x4 = -1 + (-4x) Combine like terms: (4x) + (-4x) = 0 kx2 + 0 + (4x3) + x4 = -1 + (-4x) kx2 + (4x3) + x4 = -1 + (-4x) Add '(-4x3)' to each side of the equation. kx2 + (4x3) + (-4x3) + x4 = -1 + (-4x) + (-4x3) Combine like terms: (4x3) + (-4x3) = 0 kx2 + 0 + x4 = -1 + (-4x) + (-4x3) kx2 + x4 = -1 + (-4x) + (-4x3) Add '-1x4' to each side of the equation. kx2 + x4 + -1x4 = -1 + (-4x) + (-4x3) + -1x4 Combine like terms: x4 + -1x4 = 0 kx2 + 0 = -1 + (-4x) + (-4x3) + -1x4 kx2 = -1 + (-4x) + (-4x3) + -1x4 Divide each side by 'x2'. k = -1x-2 + (-4x-1) + (-4x) + -1x2 Simplifying k = -1x-2 + (-4x-1) + (-4x) + -1x2
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