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Simplifying -5e(e + -5) + -5 = -4e + 26 Reorder the terms: -5e(-5 + e) + -5 = -4e + 26 (-5 * -5e + e * -5e) + -5 = -4e + 26 (25e + -5e2) + -5 = -4e + 26 Reorder the terms: -5 + 25e + -5e2 = -4e + 26 Reorder the terms: -5 + 25e + -5e2 = 26 + -4e Solving -5 + 25e + -5e2 = 26 + -4e Solving for variable 'e'. Reorder the terms: -5 + -26 + 25e + 4e + -5e2 = 26 + -4e + -26 + 4e Combine like terms: -5 + -26 = -31 -31 + 25e + 4e + -5e2 = 26 + -4e + -26 + 4e Combine like terms: 25e + 4e = 29e -31 + 29e + -5e2 = 26 + -4e + -26 + 4e Reorder the terms: -31 + 29e + -5e2 = 26 + -26 + -4e + 4e Combine like terms: 26 + -26 = 0 -31 + 29e + -5e2 = 0 + -4e + 4e -31 + 29e + -5e2 = -4e + 4e Combine like terms: -4e + 4e = 0 -31 + 29e + -5e2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 6.2 + -5.8e + e2 = 0 Move the constant term to the right: Add '-6.2' to each side of the equation. 6.2 + -5.8e + -6.2 + e2 = 0 + -6.2 Reorder the terms: 6.2 + -6.2 + -5.8e + e2 = 0 + -6.2 Combine like terms: 6.2 + -6.2 = 0.0 0.0 + -5.8e + e2 = 0 + -6.2 -5.8e + e2 = 0 + -6.2 Combine like terms: 0 + -6.2 = -6.2 -5.8e + e2 = -6.2 The e term is -5.8e. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8e + 8.41 + e2 = -6.2 + 8.41 Reorder the terms: 8.41 + -5.8e + e2 = -6.2 + 8.41 Combine like terms: -6.2 + 8.41 = 2.21 8.41 + -5.8e + e2 = 2.21 Factor a perfect square on the left side: (e + -2.9)(e + -2.9) = 2.21 Calculate the square root of the right side: 1.486606875 Break this problem into two subproblems by setting (e + -2.9) equal to 1.486606875 and -1.486606875.Subproblem 1
e + -2.9 = 1.486606875 Simplifying e + -2.9 = 1.486606875 Reorder the terms: -2.9 + e = 1.486606875 Solving -2.9 + e = 1.486606875 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + e = 1.486606875 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + e = 1.486606875 + 2.9 e = 1.486606875 + 2.9 Combine like terms: 1.486606875 + 2.9 = 4.386606875 e = 4.386606875 Simplifying e = 4.386606875Subproblem 2
e + -2.9 = -1.486606875 Simplifying e + -2.9 = -1.486606875 Reorder the terms: -2.9 + e = -1.486606875 Solving -2.9 + e = -1.486606875 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + e = -1.486606875 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + e = -1.486606875 + 2.9 e = -1.486606875 + 2.9 Combine like terms: -1.486606875 + 2.9 = 1.413393125 e = 1.413393125 Simplifying e = 1.413393125Solution
The solution to the problem is based on the solutions from the subproblems. e = {4.386606875, 1.413393125}
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