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Simplifying e2 + 30e + -55 = 0 Reorder the terms: -55 + 30e + e2 = 0 Solving -55 + 30e + e2 = 0 Solving for variable 'e'. Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 30e + 55 + e2 = 0 + 55 Reorder the terms: -55 + 55 + 30e + e2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 30e + e2 = 0 + 55 30e + e2 = 0 + 55 Combine like terms: 0 + 55 = 55 30e + e2 = 55 The e term is 30e. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30e + 225 + e2 = 55 + 225 Reorder the terms: 225 + 30e + e2 = 55 + 225 Combine like terms: 55 + 225 = 280 225 + 30e + e2 = 280 Factor a perfect square on the left side: (e + 15)(e + 15) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (e + 15) equal to 16.733200531 and -16.733200531.Subproblem 1
e + 15 = 16.733200531 Simplifying e + 15 = 16.733200531 Reorder the terms: 15 + e = 16.733200531 Solving 15 + e = 16.733200531 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + e = 16.733200531 + -15 Combine like terms: 15 + -15 = 0 0 + e = 16.733200531 + -15 e = 16.733200531 + -15 Combine like terms: 16.733200531 + -15 = 1.733200531 e = 1.733200531 Simplifying e = 1.733200531Subproblem 2
e + 15 = -16.733200531 Simplifying e + 15 = -16.733200531 Reorder the terms: 15 + e = -16.733200531 Solving 15 + e = -16.733200531 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + e = -16.733200531 + -15 Combine like terms: 15 + -15 = 0 0 + e = -16.733200531 + -15 e = -16.733200531 + -15 Combine like terms: -16.733200531 + -15 = -31.733200531 e = -31.733200531 Simplifying e = -31.733200531Solution
The solution to the problem is based on the solutions from the subproblems. e = {1.733200531, -31.733200531}
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