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Simplifying 4e2x + 1 = 65 Reorder the terms: 1 + 4e2x = 65 Solving 1 + 4e2x = 65 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4e2x = 65 + -1 Combine like terms: 1 + -1 = 0 0 + 4e2x = 65 + -1 4e2x = 65 + -1 Combine like terms: 65 + -1 = 64 4e2x = 64 Divide each side by '4x'. e2 = 16x-1 Simplifying e2 = 16x-1 Combine like terms: 16x-1 + -16x-1 = 0 e2 + -16x-1 = 0 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + -16) = 0Subproblem 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 + -16)' equal to zero and attempt to solve: Simplifying e2x + -16 = 0 Reorder the terms: -16 + e2x = 0 Solving -16 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + e2x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + e2x = 0 + 16 e2x = 0 + 16 Combine like terms: 0 + 16 = 16 e2x = 16 Divide each side by 'x'. e2 = 16x-1 Simplifying e2 = 16x-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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