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Simplifying e2 + 3e + -24 = 0 Reorder the terms: -24 + 3e + e2 = 0 Solving -24 + 3e + e2 = 0 Solving for variable 'e'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 3e + 24 + e2 = 0 + 24 Reorder the terms: -24 + 24 + 3e + e2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 3e + e2 = 0 + 24 3e + e2 = 0 + 24 Combine like terms: 0 + 24 = 24 3e + e2 = 24 The e term is 3e. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3e + 2.25 + e2 = 24 + 2.25 Reorder the terms: 2.25 + 3e + e2 = 24 + 2.25 Combine like terms: 24 + 2.25 = 26.25 2.25 + 3e + e2 = 26.25 Factor a perfect square on the left side: (e + 1.5)(e + 1.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (e + 1.5) equal to 5.123475383 and -5.123475383.Subproblem 1
e + 1.5 = 5.123475383 Simplifying e + 1.5 = 5.123475383 Reorder the terms: 1.5 + e = 5.123475383 Solving 1.5 + e = 5.123475383 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + e = 5.123475383 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + e = 5.123475383 + -1.5 e = 5.123475383 + -1.5 Combine like terms: 5.123475383 + -1.5 = 3.623475383 e = 3.623475383 Simplifying e = 3.623475383Subproblem 2
e + 1.5 = -5.123475383 Simplifying e + 1.5 = -5.123475383 Reorder the terms: 1.5 + e = -5.123475383 Solving 1.5 + e = -5.123475383 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + e = -5.123475383 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + e = -5.123475383 + -1.5 e = -5.123475383 + -1.5 Combine like terms: -5.123475383 + -1.5 = -6.623475383 e = -6.623475383 Simplifying e = -6.623475383Solution
The solution to the problem is based on the solutions from the subproblems. e = {3.623475383, -6.623475383}
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