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Simplifying (3e2x + 0.5x2) + -6 = 42 Remove parenthesis around (3e2x + 0.5x2) 3e2x + 0.5x2 + -6 = 42 Reorder the terms: -6 + 3e2x + 0.5x2 = 42 Solving -6 + 3e2x + 0.5x2 = 42 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 3e2x + 6 + 0.5x2 = 42 + 6 Reorder the terms: -6 + 6 + 3e2x + 0.5x2 = 42 + 6 Combine like terms: -6 + 6 = 0 0 + 3e2x + 0.5x2 = 42 + 6 3e2x + 0.5x2 = 42 + 6 Combine like terms: 42 + 6 = 48 3e2x + 0.5x2 = 48 Add '-0.5x2' to each side of the equation. 3e2x + 0.5x2 + -0.5x2 = 48 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 3e2x + 0.0 = 48 + -0.5x2 3e2x = 48 + -0.5x2 Divide each side by '3x'. e2 = 16x-1 + -0.1666666667x Simplifying e2 = 16x-1 + -0.1666666667x Reorder the terms: e2 + -16x-1 + 0.1666666667x = 16x-1 + -16x-1 + -0.1666666667x + 0.1666666667x Combine like terms: 16x-1 + -16x-1 = 0 e2 + -16x-1 + 0.1666666667x = 0 + -0.1666666667x + 0.1666666667x e2 + -16x-1 + 0.1666666667x = -0.1666666667x + 0.1666666667x Combine like terms: -0.1666666667x + 0.1666666667x = 0.0000000000 e2 + -16x-1 + 0.1666666667x = 0.0000000000 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + -16 + 0.1666666667x2) = 0.0000000000Subproblem 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 + 0.1666666667x2)' equal to zero and attempt to solve: Simplifying e2x + -16 + 0.1666666667x2 = 0 Reorder the terms: -16 + e2x + 0.1666666667x2 = 0 Solving -16 + e2x + 0.1666666667x2 = 0 Move all terms containing e to the left, all other terms to the right. Add '16' to each side of the equation. -16 + e2x + 16 + 0.1666666667x2 = 0 + 16 Reorder the terms: -16 + 16 + e2x + 0.1666666667x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + e2x + 0.1666666667x2 = 0 + 16 e2x + 0.1666666667x2 = 0 + 16 Combine like terms: 0 + 16 = 16 e2x + 0.1666666667x2 = 16 Add '-0.1666666667x2' to each side of the equation. e2x + 0.1666666667x2 + -0.1666666667x2 = 16 + -0.1666666667x2 Combine like terms: 0.1666666667x2 + -0.1666666667x2 = 0.0000000000 e2x + 0.0000000000 = 16 + -0.1666666667x2 e2x = 16 + -0.1666666667x2 Divide each side by 'x'. e2 = 16x-1 + -0.1666666667x Simplifying e2 = 16x-1 + -0.1666666667x 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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