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Simplifying 20(5e) + -471 + 2e2 = e Remove parenthesis around (5e) 20 * 5e + -471 + 2e2 = e Multiply 20 * 5 100e + -471 + 2e2 = e Reorder the terms: -471 + 100e + 2e2 = e Solving -471 + 100e + 2e2 = e Solving for variable 'e'. Reorder the terms: -471 + 100e + -1e + 2e2 = e + -1e Combine like terms: 100e + -1e = 99e -471 + 99e + 2e2 = e + -1e Combine like terms: e + -1e = 0 -471 + 99e + 2e2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -235.5 + 49.5e + e2 = 0 Move the constant term to the right: Add '235.5' to each side of the equation. -235.5 + 49.5e + 235.5 + e2 = 0 + 235.5 Reorder the terms: -235.5 + 235.5 + 49.5e + e2 = 0 + 235.5 Combine like terms: -235.5 + 235.5 = 0.0 0.0 + 49.5e + e2 = 0 + 235.5 49.5e + e2 = 0 + 235.5 Combine like terms: 0 + 235.5 = 235.5 49.5e + e2 = 235.5 The e term is 49.5e. Take half its coefficient (24.75). Square it (612.5625) and add it to both sides. Add '612.5625' to each side of the equation. 49.5e + 612.5625 + e2 = 235.5 + 612.5625 Reorder the terms: 612.5625 + 49.5e + e2 = 235.5 + 612.5625 Combine like terms: 235.5 + 612.5625 = 848.0625 612.5625 + 49.5e + e2 = 848.0625 Factor a perfect square on the left side: (e + 24.75)(e + 24.75) = 848.0625 Calculate the square root of the right side: 29.121512667 Break this problem into two subproblems by setting (e + 24.75) equal to 29.121512667 and -29.121512667.Subproblem 1
e + 24.75 = 29.121512667 Simplifying e + 24.75 = 29.121512667 Reorder the terms: 24.75 + e = 29.121512667 Solving 24.75 + e = 29.121512667 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-24.75' to each side of the equation. 24.75 + -24.75 + e = 29.121512667 + -24.75 Combine like terms: 24.75 + -24.75 = 0.00 0.00 + e = 29.121512667 + -24.75 e = 29.121512667 + -24.75 Combine like terms: 29.121512667 + -24.75 = 4.371512667 e = 4.371512667 Simplifying e = 4.371512667Subproblem 2
e + 24.75 = -29.121512667 Simplifying e + 24.75 = -29.121512667 Reorder the terms: 24.75 + e = -29.121512667 Solving 24.75 + e = -29.121512667 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-24.75' to each side of the equation. 24.75 + -24.75 + e = -29.121512667 + -24.75 Combine like terms: 24.75 + -24.75 = 0.00 0.00 + e = -29.121512667 + -24.75 e = -29.121512667 + -24.75 Combine like terms: -29.121512667 + -24.75 = -53.871512667 e = -53.871512667 Simplifying e = -53.871512667Solution
The solution to the problem is based on the solutions from the subproblems. e = {4.371512667, -53.871512667}
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