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Simplifying 1 + e2x = 5e2x Solving 1 + e2x = 5e2x Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-5e2x' to each side of the equation. 1 + e2x + -5e2x = 5e2x + -5e2x Combine like terms: e2x + -5e2x = -4e2x 1 + -4e2x = 5e2x + -5e2x Combine like terms: 5e2x + -5e2x = 0 1 + -4e2x = 0 Add '-1' to each side of the equation. 1 + -1 + -4e2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4e2x = 0 + -1 -4e2x = 0 + -1 Combine like terms: 0 + -1 = -1 -4e2x = -1 Divide each side by '-4x'. e2 = 0.25x-1 Simplifying e2 = 0.25x-1 Combine like terms: 0.25x-1 + -0.25x-1 = 0.00 e2 + -0.25x-1 = 0.00 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + -0.25) = 0.00Subproblem 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 + -0.25)' equal to zero and attempt to solve: Simplifying e2x + -0.25 = 0 Reorder the terms: -0.25 + e2x = 0 Solving -0.25 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + e2x = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + e2x = 0 + 0.25 e2x = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 e2x = 0.25 Divide each side by 'x'. e2 = 0.25x-1 Simplifying e2 = 0.25x-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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