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Simplifying x4 = 2x3 + 24x2 Reorder the terms: x4 = 24x2 + 2x3 Solving x4 = 24x2 + 2x3 Solving for variable 'x'. Reorder the terms: -24x2 + -2x3 + x4 = 24x2 + 2x3 + -24x2 + -2x3 Reorder the terms: -24x2 + -2x3 + x4 = 24x2 + -24x2 + 2x3 + -2x3 Combine like terms: 24x2 + -24x2 = 0 -24x2 + -2x3 + x4 = 0 + 2x3 + -2x3 -24x2 + -2x3 + x4 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -24x2 + -2x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-24 + -2x + x2) = 0 Factor a trinomial. x2((-4 + -1x)(6 + -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 '(-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 = -4Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, -4, 6}
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