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Simplifying 3x4 + 10x3 + 13x2 + 6k + 1 = 0 Reorder the terms: 1 + 6k + 13x2 + 10x3 + 3x4 = 0 Solving 1 + 6k + 13x2 + 10x3 + 3x4 = 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 + 6k + 13x2 + 10x3 + -1 + 3x4 = 0 + -1 Reorder the terms: 1 + -1 + 6k + 13x2 + 10x3 + 3x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6k + 13x2 + 10x3 + 3x4 = 0 + -1 6k + 13x2 + 10x3 + 3x4 = 0 + -1 Combine like terms: 0 + -1 = -1 6k + 13x2 + 10x3 + 3x4 = -1 Add '-13x2' to each side of the equation. 6k + 13x2 + 10x3 + -13x2 + 3x4 = -1 + -13x2 Reorder the terms: 6k + 13x2 + -13x2 + 10x3 + 3x4 = -1 + -13x2 Combine like terms: 13x2 + -13x2 = 0 6k + 0 + 10x3 + 3x4 = -1 + -13x2 6k + 10x3 + 3x4 = -1 + -13x2 Add '-10x3' to each side of the equation. 6k + 10x3 + -10x3 + 3x4 = -1 + -13x2 + -10x3 Combine like terms: 10x3 + -10x3 = 0 6k + 0 + 3x4 = -1 + -13x2 + -10x3 6k + 3x4 = -1 + -13x2 + -10x3 Add '-3x4' to each side of the equation. 6k + 3x4 + -3x4 = -1 + -13x2 + -10x3 + -3x4 Combine like terms: 3x4 + -3x4 = 0 6k + 0 = -1 + -13x2 + -10x3 + -3x4 6k = -1 + -13x2 + -10x3 + -3x4 Divide each side by '6'. k = -0.1666666667 + -2.166666667x2 + -1.666666667x3 + -0.5x4 Simplifying k = -0.1666666667 + -2.166666667x2 + -1.666666667x3 + -0.5x4
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