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Simplifying (e2) + -209e + 100 = 0 e2 + -209e + 100 = 0 Reorder the terms: 100 + -209e + e2 = 0 Solving 100 + -209e + e2 = 0 Solving for variable 'e'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -209e + -100 + e2 = 0 + -100 Reorder the terms: 100 + -100 + -209e + e2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -209e + e2 = 0 + -100 -209e + e2 = 0 + -100 Combine like terms: 0 + -100 = -100 -209e + e2 = -100 The e term is -209e. Take half its coefficient (-104.5). Square it (10920.25) and add it to both sides. Add '10920.25' to each side of the equation. -209e + 10920.25 + e2 = -100 + 10920.25 Reorder the terms: 10920.25 + -209e + e2 = -100 + 10920.25 Combine like terms: -100 + 10920.25 = 10820.25 10920.25 + -209e + e2 = 10820.25 Factor a perfect square on the left side: (e + -104.5)(e + -104.5) = 10820.25 Calculate the square root of the right side: 104.020430686 Break this problem into two subproblems by setting (e + -104.5) equal to 104.020430686 and -104.020430686.Subproblem 1
e + -104.5 = 104.020430686 Simplifying e + -104.5 = 104.020430686 Reorder the terms: -104.5 + e = 104.020430686 Solving -104.5 + e = 104.020430686 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '104.5' to each side of the equation. -104.5 + 104.5 + e = 104.020430686 + 104.5 Combine like terms: -104.5 + 104.5 = 0.0 0.0 + e = 104.020430686 + 104.5 e = 104.020430686 + 104.5 Combine like terms: 104.020430686 + 104.5 = 208.520430686 e = 208.520430686 Simplifying e = 208.520430686Subproblem 2
e + -104.5 = -104.020430686 Simplifying e + -104.5 = -104.020430686 Reorder the terms: -104.5 + e = -104.020430686 Solving -104.5 + e = -104.020430686 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '104.5' to each side of the equation. -104.5 + 104.5 + e = -104.020430686 + 104.5 Combine like terms: -104.5 + 104.5 = 0.0 0.0 + e = -104.020430686 + 104.5 e = -104.020430686 + 104.5 Combine like terms: -104.020430686 + 104.5 = 0.479569314 e = 0.479569314 Simplifying e = 0.479569314Solution
The solution to the problem is based on the solutions from the subproblems. e = {208.520430686, 0.479569314}
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