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Simplifying e13x + -5e8x + -2e3x = 0 Reorder the terms: -2e3x + -5e8x + e13x = 0 Solving -2e3x + -5e8x + e13x = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), 'e3x'. e3x(-2 + -5e5 + e10) = 0Subproblem 1
Set the factor 'e3x' equal to zero and attempt to solve: Simplifying e3x = 0 Solving e3x = 0 Move all terms containing e to the left, all other terms to the right. Simplifying e3x = 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 '(-2 + -5e5 + e10)' equal to zero and attempt to solve: Simplifying -2 + -5e5 + e10 = 0 Solving -2 + -5e5 + e10 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -5e5 + 2 + e10 = 0 + 2 Reorder the terms: -2 + 2 + -5e5 + e10 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5e5 + e10 = 0 + 2 -5e5 + e10 = 0 + 2 Combine like terms: 0 + 2 = 2 -5e5 + e10 = 2 The e term is -5e5. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5e5 + 6.25 + e10 = 2 + 6.25 Reorder the terms: 6.25 + -5e5 + e10 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + -5e5 + e10 = 8.25 Factor a perfect square on the left side: (e5 + -2.5)(e5 + -2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (e5 + -2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
e5 + -2.5 = 2.872281323 Simplifying e5 + -2.5 = 2.872281323 Reorder the terms: -2.5 + e5 = 2.872281323 Solving -2.5 + e5 = 2.872281323 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + e5 = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + e5 = 2.872281323 + 2.5 e5 = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 e5 = 5.372281323 Simplifying e5 = 5.372281323 Reorder the terms: -5.372281323 + e5 = 5.372281323 + -5.372281323 Combine like terms: 5.372281323 + -5.372281323 = 0.000000000 -5.372281323 + e5 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
e5 + -2.5 = -2.872281323 Simplifying e5 + -2.5 = -2.872281323 Reorder the terms: -2.5 + e5 = -2.872281323 Solving -2.5 + e5 = -2.872281323 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + e5 = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + e5 = -2.872281323 + 2.5 e5 = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 e5 = -0.372281323 Simplifying e5 = -0.372281323 Reorder the terms: 0.372281323 + e5 = -0.372281323 + 0.372281323 Combine like terms: -0.372281323 + 0.372281323 = 0.000000000 0.372281323 + e5 = 0.000000000 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. 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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