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Simplifying 6x4 = 5x3 + -1x2 Reorder the terms: 6x4 = -1x2 + 5x3 Solving 6x4 = -1x2 + 5x3 Solving for variable 'x'. Reorder the terms: x2 + -5x3 + 6x4 = -1x2 + 5x3 + x2 + -5x3 Reorder the terms: x2 + -5x3 + 6x4 = -1x2 + x2 + 5x3 + -5x3 Combine like terms: -1x2 + x2 = 0 x2 + -5x3 + 6x4 = 0 + 5x3 + -5x3 x2 + -5x3 + 6x4 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 x2 + -5x3 + 6x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(1 + -5x + 6x2) = 0 Factor a trinomial. x2((1 + -3x)(1 + -2x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {0, 0.3333333333, 0.5}
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