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Simplifying x2 + 3x + -86 = 0 Reorder the terms: -86 + 3x + x2 = 0 Solving -86 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + 3x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + 3x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 3x + x2 = 0 + 86 3x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 3x + x2 = 86 The x term is 3x. 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. 3x + 2.25 + x2 = 86 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 86 + 2.25 Combine like terms: 86 + 2.25 = 88.25 2.25 + 3x + x2 = 88.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (x + 1.5) equal to 9.394147114 and -9.394147114.Subproblem 1
x + 1.5 = 9.394147114 Simplifying x + 1.5 = 9.394147114 Reorder the terms: 1.5 + x = 9.394147114 Solving 1.5 + x = 9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.394147114 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.394147114 + -1.5 x = 9.394147114 + -1.5 Combine like terms: 9.394147114 + -1.5 = 7.894147114 x = 7.894147114 Simplifying x = 7.894147114Subproblem 2
x + 1.5 = -9.394147114 Simplifying x + 1.5 = -9.394147114 Reorder the terms: 1.5 + x = -9.394147114 Solving 1.5 + x = -9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.394147114 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.394147114 + -1.5 x = -9.394147114 + -1.5 Combine like terms: -9.394147114 + -1.5 = -10.894147114 x = -10.894147114 Simplifying x = -10.894147114Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.894147114, -10.894147114}
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