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Simplifying x2 + 7(3 + 2x) + -2x(1 + 3k) = 0 x2 + (3 * 7 + 2x * 7) + -2x(1 + 3k) = 0 x2 + (21 + 14x) + -2x(1 + 3k) = 0 x2 + 21 + 14x + (1 * -2x + 3k * -2x) = 0 Reorder the terms: x2 + 21 + 14x + (-6kx + -2x) = 0 x2 + 21 + 14x + (-6kx + -2x) = 0 Reorder the terms: 21 + -6kx + 14x + -2x + x2 = 0 Combine like terms: 14x + -2x = 12x 21 + -6kx + 12x + x2 = 0 Solving 21 + -6kx + 12x + x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -6kx + 12x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -6kx + 12x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -6kx + 12x + x2 = 0 + -21 -6kx + 12x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -6kx + 12x + x2 = -21 Add '-12x' to each side of the equation. -6kx + 12x + -12x + x2 = -21 + -12x Combine like terms: 12x + -12x = 0 -6kx + 0 + x2 = -21 + -12x -6kx + x2 = -21 + -12x Add '-1x2' to each side of the equation. -6kx + x2 + -1x2 = -21 + -12x + -1x2 Combine like terms: x2 + -1x2 = 0 -6kx + 0 = -21 + -12x + -1x2 -6kx = -21 + -12x + -1x2 Divide each side by '-6x'. k = 3.5x-1 + 2 + 0.1666666667x Simplifying k = 3.5x-1 + 2 + 0.1666666667x Reorder the terms: k = 2 + 3.5x-1 + 0.1666666667x
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