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Simplifying x4 = 2x3 + 8x2 Reorder the terms: x4 = 8x2 + 2x3 Solving x4 = 8x2 + 2x3 Solving for variable 'x'. Reorder the terms: -8x2 + -2x3 + x4 = 8x2 + 2x3 + -8x2 + -2x3 Reorder the terms: -8x2 + -2x3 + x4 = 8x2 + -8x2 + 2x3 + -2x3 Combine like terms: 8x2 + -8x2 = 0 -8x2 + -2x3 + x4 = 0 + 2x3 + -2x3 -8x2 + -2x3 + x4 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -8x2 + -2x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-8 + -2x + x2) = 0 Factor a trinomial. x2((-2 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, -2, 4}
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