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Simplifying 3e2x + 5 = 1000 Reorder the terms: 5 + 3e2x = 1000 Solving 5 + 3e2x = 1000 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3e2x = 1000 + -5 Combine like terms: 5 + -5 = 0 0 + 3e2x = 1000 + -5 3e2x = 1000 + -5 Combine like terms: 1000 + -5 = 995 3e2x = 995 Divide each side by '3x'. e2 = 331.6666667x-1 Simplifying e2 = 331.6666667x-1 Combine like terms: 331.6666667x-1 + -331.6666667x-1 = 0.0000000 e2 + -331.6666667x-1 = 0.0000000 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + -331.6666667) = 0.0000000Subproblem 1
Set the factor 'x-1' equal to zero and attempt to solve: Simplifying x-1 = 0 Solving x-1 = 0 Move all terms containing e to the left, all other terms to the right. Add '-1x-1' to each side of the equation. x-1 + -1x-1 = 0 + -1x-1 Remove the zero: 0 = -1x-1 Simplifying 0 = -1x-1 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 '(e2x + -331.6666667)' equal to zero and attempt to solve: Simplifying e2x + -331.6666667 = 0 Reorder the terms: -331.6666667 + e2x = 0 Solving -331.6666667 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '331.6666667' to each side of the equation. -331.6666667 + 331.6666667 + e2x = 0 + 331.6666667 Combine like terms: -331.6666667 + 331.6666667 = 0.0000000 0.0000000 + e2x = 0 + 331.6666667 e2x = 0 + 331.6666667 Combine like terms: 0 + 331.6666667 = 331.6666667 e2x = 331.6666667 Divide each side by 'x'. e2 = 331.6666667x-1 Simplifying e2 = 331.6666667x-1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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