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Simplifying 2x2 + -1(2k + 1) * x + 3 + -1 = 0 Reorder the terms: 2x2 + -1(1 + 2k) * x + 3 + -1 = 0 Reorder the terms for easier multiplication: 2x2 + -1x(1 + 2k) + 3 + -1 = 0 2x2 + (1 * -1x + 2k * -1x) + 3 + -1 = 0 Reorder the terms: 2x2 + (-2kx + -1x) + 3 + -1 = 0 2x2 + (-2kx + -1x) + 3 + -1 = 0 Reorder the terms: 3 + -1 + -2kx + -1x + 2x2 = 0 Combine like terms: 3 + -1 = 2 2 + -2kx + -1x + 2x2 = 0 Solving 2 + -2kx + -1x + 2x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2kx + -1x + -2 + 2x2 = 0 + -2 Reorder the terms: 2 + -2 + -2kx + -1x + 2x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2kx + -1x + 2x2 = 0 + -2 -2kx + -1x + 2x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2kx + -1x + 2x2 = -2 Add 'x' to each side of the equation. -2kx + -1x + x + 2x2 = -2 + x Combine like terms: -1x + x = 0 -2kx + 0 + 2x2 = -2 + x -2kx + 2x2 = -2 + x Add '-2x2' to each side of the equation. -2kx + 2x2 + -2x2 = -2 + x + -2x2 Combine like terms: 2x2 + -2x2 = 0 -2kx + 0 = -2 + x + -2x2 -2kx = -2 + x + -2x2 Divide each side by '-2x'. k = x-1 + -0.5 + x Simplifying k = x-1 + -0.5 + x Reorder the terms: k = -0.5 + x-1 + x
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