(x^2-2x+1)e^2x=0

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Solution for (x^2-2x+1)e^2x=0 equation:


Simplifying
(x2 + -2x + 1) * e2x = 0

Reorder the terms:
(1 + -2x + x2) * e2x = 0

Reorder the terms for easier multiplication:
e2x(1 + -2x + x2) = 0
(1 * e2x + -2x * e2x + x2 * e2x) = 0
(1e2x + -2e2x2 + e2x3) = 0

Solving
1e2x + -2e2x2 + e2x3 = 0

Solving for variable 'e'.

Move all terms containing e to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'e2x'.
e2x(1 + -2x + x2) = 0

Factor a trinomial.
e2x((1 + -1x)(1 + -1x)) = 0

Subproblem 1

Set the factor 'e2x' equal to zero and attempt to solve: Simplifying e2x = 0 Solving e2x = 0 Move all terms containing e to the left, all other terms to the right. Simplifying e2x = 0 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing e to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing e to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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