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Simplifying 5x2 + 3e2x = 3 Reorder the terms: 3e2x + 5x2 = 3 Solving 3e2x + 5x2 = 3 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-5x2' to each side of the equation. 3e2x + 5x2 + -5x2 = 3 + -5x2 Combine like terms: 5x2 + -5x2 = 0 3e2x + 0 = 3 + -5x2 3e2x = 3 + -5x2 Divide each side by '3x'. e2 = x-1 + -1.666666667x Simplifying e2 = x-1 + -1.666666667x Reorder the terms: e2 + -1x-1 + 1.666666667x = x-1 + -1x-1 + -1.666666667x + 1.666666667x Combine like terms: x-1 + -1x-1 = 0 e2 + -1x-1 + 1.666666667x = 0 + -1.666666667x + 1.666666667x e2 + -1x-1 + 1.666666667x = -1.666666667x + 1.666666667x Combine like terms: -1.666666667x + 1.666666667x = 0.000000000 e2 + -1x-1 + 1.666666667x = 0.000000000 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + -1 + 1.666666667x2) = 0.000000000Subproblem 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 + -1 + 1.666666667x2)' equal to zero and attempt to solve: Simplifying e2x + -1 + 1.666666667x2 = 0 Reorder the terms: -1 + e2x + 1.666666667x2 = 0 Solving -1 + e2x + 1.666666667x2 = 0 Move all terms containing e to the left, all other terms to the right. Add '1' to each side of the equation. -1 + e2x + 1 + 1.666666667x2 = 0 + 1 Reorder the terms: -1 + 1 + e2x + 1.666666667x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + e2x + 1.666666667x2 = 0 + 1 e2x + 1.666666667x2 = 0 + 1 Combine like terms: 0 + 1 = 1 e2x + 1.666666667x2 = 1 Add '-1.666666667x2' to each side of the equation. e2x + 1.666666667x2 + -1.666666667x2 = 1 + -1.666666667x2 Combine like terms: 1.666666667x2 + -1.666666667x2 = 0.000000000 e2x + 0.000000000 = 1 + -1.666666667x2 e2x = 1 + -1.666666667x2 Divide each side by 'x'. e2 = x-1 + -1.666666667x Simplifying e2 = x-1 + -1.666666667x 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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