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Simplifying kx2 + 4x2 + -1kx + x + 1 = 0 Reorder the terms: 1 + -1kx + kx2 + x + 4x2 = 0 Solving 1 + -1kx + kx2 + x + 4x2 = 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 + -1kx + kx2 + x + -1 + 4x2 = 0 + -1 Reorder the terms: 1 + -1 + -1kx + kx2 + x + 4x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1kx + kx2 + x + 4x2 = 0 + -1 -1kx + kx2 + x + 4x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1kx + kx2 + x + 4x2 = -1 Add '-1x' to each side of the equation. -1kx + kx2 + x + -1x + 4x2 = -1 + -1x Combine like terms: x + -1x = 0 -1kx + kx2 + 0 + 4x2 = -1 + -1x -1kx + kx2 + 4x2 = -1 + -1x Add '-4x2' to each side of the equation. -1kx + kx2 + 4x2 + -4x2 = -1 + -1x + -4x2 Combine like terms: 4x2 + -4x2 = 0 -1kx + kx2 + 0 = -1 + -1x + -4x2 -1kx + kx2 = -1 + -1x + -4x2 Reorder the terms: 1 + -1kx + kx2 + x + 4x2 = -1 + -1x + -4x2 + 1 + x + 4x2 Reorder the terms: 1 + -1kx + kx2 + x + 4x2 = -1 + 1 + -1x + x + -4x2 + 4x2 Combine like terms: -1 + 1 = 0 1 + -1kx + kx2 + x + 4x2 = 0 + -1x + x + -4x2 + 4x2 1 + -1kx + kx2 + x + 4x2 = -1x + x + -4x2 + 4x2 Combine like terms: -1x + x = 0 1 + -1kx + kx2 + x + 4x2 = 0 + -4x2 + 4x2 1 + -1kx + kx2 + x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 1 + -1kx + kx2 + x + 4x2 = 0 The solution to this equation could not be determined.
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