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Simplifying 17x6 = 17x5 + 204x4 Reorder the terms: 17x6 = 204x4 + 17x5 Solving 17x6 = 204x4 + 17x5 Solving for variable 'x'. Reorder the terms: -204x4 + -17x5 + 17x6 = 204x4 + 17x5 + -204x4 + -17x5 Reorder the terms: -204x4 + -17x5 + 17x6 = 204x4 + -204x4 + 17x5 + -17x5 Combine like terms: 204x4 + -204x4 = 0 -204x4 + -17x5 + 17x6 = 0 + 17x5 + -17x5 -204x4 + -17x5 + 17x6 = 17x5 + -17x5 Combine like terms: 17x5 + -17x5 = 0 -204x4 + -17x5 + 17x6 = 0 Factor out the Greatest Common Factor (GCF), '17x4'. 17x4(-12 + -1x + x2) = 0 Factor a trinomial. 17x4((-3 + -1x)(4 + -1x)) = 0 Ignore the factor 17.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 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 = {-3, 4}
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