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Simplifying 2e2 + 12e + -22 = 0 Reorder the terms: -22 + 12e + 2e2 = 0 Solving -22 + 12e + 2e2 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 6e + e2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 6e + e2)' equal to zero and attempt to solve: Simplifying -11 + 6e + e2 = 0 Solving -11 + 6e + e2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 6e + 11 + e2 = 0 + 11 Reorder the terms: -11 + 11 + 6e + e2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6e + e2 = 0 + 11 6e + e2 = 0 + 11 Combine like terms: 0 + 11 = 11 6e + e2 = 11 The e term is 6e. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6e + 9 + e2 = 11 + 9 Reorder the terms: 9 + 6e + e2 = 11 + 9 Combine like terms: 11 + 9 = 20 9 + 6e + e2 = 20 Factor a perfect square on the left side: (e + 3)(e + 3) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (e + 3) equal to 4.472135955 and -4.472135955.Subproblem 1
e + 3 = 4.472135955 Simplifying e + 3 = 4.472135955 Reorder the terms: 3 + e = 4.472135955 Solving 3 + e = 4.472135955 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + e = 4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + e = 4.472135955 + -3 e = 4.472135955 + -3 Combine like terms: 4.472135955 + -3 = 1.472135955 e = 1.472135955 Simplifying e = 1.472135955Subproblem 2
e + 3 = -4.472135955 Simplifying e + 3 = -4.472135955 Reorder the terms: 3 + e = -4.472135955 Solving 3 + e = -4.472135955 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + e = -4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + e = -4.472135955 + -3 e = -4.472135955 + -3 Combine like terms: -4.472135955 + -3 = -7.472135955 e = -7.472135955 Simplifying e = -7.472135955Solution
The solution to the problem is based on the solutions from the subproblems. e = {1.472135955, -7.472135955}Solution
e = {1.472135955, -7.472135955}
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