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Simplifying x4 + -2x3 = x3 + 10x2 Reorder the terms: -2x3 + x4 = x3 + 10x2 Reorder the terms: -2x3 + x4 = 10x2 + x3 Solving -2x3 + x4 = 10x2 + x3 Solving for variable 'x'. Reorder the terms: -10x2 + -2x3 + -1x3 + x4 = 10x2 + x3 + -10x2 + -1x3 Combine like terms: -2x3 + -1x3 = -3x3 -10x2 + -3x3 + x4 = 10x2 + x3 + -10x2 + -1x3 Reorder the terms: -10x2 + -3x3 + x4 = 10x2 + -10x2 + x3 + -1x3 Combine like terms: 10x2 + -10x2 = 0 -10x2 + -3x3 + x4 = 0 + x3 + -1x3 -10x2 + -3x3 + x4 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -10x2 + -3x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-10 + -3x + x2) = 0 Factor a trinomial. x2((-2 + -1x)(5 + -1x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, -2, 5}
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