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Simplifying 12x2 + -4e2x + -2 = 0 Reorder the terms: -2 + -4e2x + 12x2 = 0 Solving -2 + -4e2x + 12x2 = 0 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -4e2x + 2 + 12x2 = 0 + 2 Reorder the terms: -2 + 2 + -4e2x + 12x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4e2x + 12x2 = 0 + 2 -4e2x + 12x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4e2x + 12x2 = 2 Add '-12x2' to each side of the equation. -4e2x + 12x2 + -12x2 = 2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -4e2x + 0 = 2 + -12x2 -4e2x = 2 + -12x2 Divide each side by '-4x'. e2 = -0.5x-1 + 3x Simplifying e2 = -0.5x-1 + 3x Reorder the terms: e2 + 0.5x-1 + -3x = -0.5x-1 + 0.5x-1 + 3x + -3x Combine like terms: -0.5x-1 + 0.5x-1 = 0.0 e2 + 0.5x-1 + -3x = 0.0 + 3x + -3x e2 + 0.5x-1 + -3x = 3x + -3x Combine like terms: 3x + -3x = 0 e2 + 0.5x-1 + -3x = 0 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + 0.5 + -3x2) = 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 + 0.5 + -3x2)' equal to zero and attempt to solve: Simplifying e2x + 0.5 + -3x2 = 0 Reorder the terms: 0.5 + e2x + -3x2 = 0 Solving 0.5 + e2x + -3x2 = 0 Move all terms containing e to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + e2x + -0.5 + -3x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + e2x + -3x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + e2x + -3x2 = 0 + -0.5 e2x + -3x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 e2x + -3x2 = -0.5 Add '3x2' to each side of the equation. e2x + -3x2 + 3x2 = -0.5 + 3x2 Combine like terms: -3x2 + 3x2 = 0 e2x + 0 = -0.5 + 3x2 e2x = -0.5 + 3x2 Divide each side by 'x'. e2 = -0.5x-1 + 3x Simplifying e2 = -0.5x-1 + 3x 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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