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Simplifying -2e2 + -26e + 10 = 0 Reorder the terms: 10 + -26e + -2e2 = 0 Solving 10 + -26e + -2e2 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -13e + -1e2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -13e + -1e2)' equal to zero and attempt to solve: Simplifying 5 + -13e + -1e2 = 0 Solving 5 + -13e + -1e2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 13e + e2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 13e + 5 + e2 = 0 + 5 Reorder the terms: -5 + 5 + 13e + e2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 13e + e2 = 0 + 5 13e + e2 = 0 + 5 Combine like terms: 0 + 5 = 5 13e + e2 = 5 The e term is 13e. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13e + 42.25 + e2 = 5 + 42.25 Reorder the terms: 42.25 + 13e + e2 = 5 + 42.25 Combine like terms: 5 + 42.25 = 47.25 42.25 + 13e + e2 = 47.25 Factor a perfect square on the left side: (e + 6.5)(e + 6.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (e + 6.5) equal to 6.873863542 and -6.873863542.Subproblem 1
e + 6.5 = 6.873863542 Simplifying e + 6.5 = 6.873863542 Reorder the terms: 6.5 + e = 6.873863542 Solving 6.5 + e = 6.873863542 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + e = 6.873863542 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + e = 6.873863542 + -6.5 e = 6.873863542 + -6.5 Combine like terms: 6.873863542 + -6.5 = 0.373863542 e = 0.373863542 Simplifying e = 0.373863542Subproblem 2
e + 6.5 = -6.873863542 Simplifying e + 6.5 = -6.873863542 Reorder the terms: 6.5 + e = -6.873863542 Solving 6.5 + e = -6.873863542 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + e = -6.873863542 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + e = -6.873863542 + -6.5 e = -6.873863542 + -6.5 Combine like terms: -6.873863542 + -6.5 = -13.373863542 e = -13.373863542 Simplifying e = -13.373863542Solution
The solution to the problem is based on the solutions from the subproblems. e = {0.373863542, -13.373863542}Solution
e = {0.373863542, -13.373863542}
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