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Simplifying 4x2 + -3x + 2kx + 1 = 0 Reorder the terms: 1 + 2kx + -3x + 4x2 = 0 Solving 1 + 2kx + -3x + 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 + 2kx + -3x + -1 + 4x2 = 0 + -1 Reorder the terms: 1 + -1 + 2kx + -3x + 4x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2kx + -3x + 4x2 = 0 + -1 2kx + -3x + 4x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2kx + -3x + 4x2 = -1 Add '3x' to each side of the equation. 2kx + -3x + 3x + 4x2 = -1 + 3x Combine like terms: -3x + 3x = 0 2kx + 0 + 4x2 = -1 + 3x 2kx + 4x2 = -1 + 3x Add '-4x2' to each side of the equation. 2kx + 4x2 + -4x2 = -1 + 3x + -4x2 Combine like terms: 4x2 + -4x2 = 0 2kx + 0 = -1 + 3x + -4x2 2kx = -1 + 3x + -4x2 Divide each side by '2x'. k = -0.5x-1 + 1.5 + -2x Simplifying k = -0.5x-1 + 1.5 + -2x Reorder the terms: k = 1.5 + -0.5x-1 + -2x
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