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Simplifying x2 + 5x + -108 = 0 Reorder the terms: -108 + 5x + x2 = 0 Solving -108 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + 5x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 5x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 5x + x2 = 0 + 108 5x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 5x + x2 = 108 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 108 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 108 + 6.25 Combine like terms: 108 + 6.25 = 114.25 6.25 + 5x + x2 = 114.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (x + 2.5) equal to 10.688779163 and -10.688779163.Subproblem 1
x + 2.5 = 10.688779163 Simplifying x + 2.5 = 10.688779163 Reorder the terms: 2.5 + x = 10.688779163 Solving 2.5 + x = 10.688779163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.688779163 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.688779163 + -2.5 x = 10.688779163 + -2.5 Combine like terms: 10.688779163 + -2.5 = 8.188779163 x = 8.188779163 Simplifying x = 8.188779163Subproblem 2
x + 2.5 = -10.688779163 Simplifying x + 2.5 = -10.688779163 Reorder the terms: 2.5 + x = -10.688779163 Solving 2.5 + x = -10.688779163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.688779163 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.688779163 + -2.5 x = -10.688779163 + -2.5 Combine like terms: -10.688779163 + -2.5 = -13.188779163 x = -13.188779163 Simplifying x = -13.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.188779163, -13.188779163}
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