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Simplifying 65e2 + -96e + 32 = 0 Reorder the terms: 32 + -96e + 65e2 = 0 Solving 32 + -96e + 65e2 = 0 Solving for variable 'e'. Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. 0.4923076923 + -1.476923077e + e2 = 0 Move the constant term to the right: Add '-0.4923076923' to each side of the equation. 0.4923076923 + -1.476923077e + -0.4923076923 + e2 = 0 + -0.4923076923 Reorder the terms: 0.4923076923 + -0.4923076923 + -1.476923077e + e2 = 0 + -0.4923076923 Combine like terms: 0.4923076923 + -0.4923076923 = 0.0000000000 0.0000000000 + -1.476923077e + e2 = 0 + -0.4923076923 -1.476923077e + e2 = 0 + -0.4923076923 Combine like terms: 0 + -0.4923076923 = -0.4923076923 -1.476923077e + e2 = -0.4923076923 The e term is -1.476923077e. Take half its coefficient (-0.7384615385). Square it (0.5453254438) and add it to both sides. Add '0.5453254438' to each side of the equation. -1.476923077e + 0.5453254438 + e2 = -0.4923076923 + 0.5453254438 Reorder the terms: 0.5453254438 + -1.476923077e + e2 = -0.4923076923 + 0.5453254438 Combine like terms: -0.4923076923 + 0.5453254438 = 0.0530177515 0.5453254438 + -1.476923077e + e2 = 0.0530177515 Factor a perfect square on the left side: (e + -0.7384615385)(e + -0.7384615385) = 0.0530177515 Calculate the square root of the right side: 0.230255839 Break this problem into two subproblems by setting (e + -0.7384615385) equal to 0.230255839 and -0.230255839.Subproblem 1
e + -0.7384615385 = 0.230255839 Simplifying e + -0.7384615385 = 0.230255839 Reorder the terms: -0.7384615385 + e = 0.230255839 Solving -0.7384615385 + e = 0.230255839 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '0.7384615385' to each side of the equation. -0.7384615385 + 0.7384615385 + e = 0.230255839 + 0.7384615385 Combine like terms: -0.7384615385 + 0.7384615385 = 0.0000000000 0.0000000000 + e = 0.230255839 + 0.7384615385 e = 0.230255839 + 0.7384615385 Combine like terms: 0.230255839 + 0.7384615385 = 0.9687173775 e = 0.9687173775 Simplifying e = 0.9687173775Subproblem 2
e + -0.7384615385 = -0.230255839 Simplifying e + -0.7384615385 = -0.230255839 Reorder the terms: -0.7384615385 + e = -0.230255839 Solving -0.7384615385 + e = -0.230255839 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '0.7384615385' to each side of the equation. -0.7384615385 + 0.7384615385 + e = -0.230255839 + 0.7384615385 Combine like terms: -0.7384615385 + 0.7384615385 = 0.0000000000 0.0000000000 + e = -0.230255839 + 0.7384615385 e = -0.230255839 + 0.7384615385 Combine like terms: -0.230255839 + 0.7384615385 = 0.5082056995 e = 0.5082056995 Simplifying e = 0.5082056995Solution
The solution to the problem is based on the solutions from the subproblems. e = {0.9687173775, 0.5082056995}
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