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Simplifying x2 + -19x + -83 = 81 Reorder the terms: -83 + -19x + x2 = 81 Solving -83 + -19x + x2 = 81 Solving for variable 'x'. Reorder the terms: -83 + -81 + -19x + x2 = 81 + -81 Combine like terms: -83 + -81 = -164 -164 + -19x + x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -164 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + -19x + 164 + x2 = 0 + 164 Reorder the terms: -164 + 164 + -19x + x2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + -19x + x2 = 0 + 164 -19x + x2 = 0 + 164 Combine like terms: 0 + 164 = 164 -19x + x2 = 164 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 164 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 164 + 90.25 Combine like terms: 164 + 90.25 = 254.25 90.25 + -19x + x2 = 254.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 254.25 Calculate the square root of the right side: 15.945218719 Break this problem into two subproblems by setting (x + -9.5) equal to 15.945218719 and -15.945218719.Subproblem 1
x + -9.5 = 15.945218719 Simplifying x + -9.5 = 15.945218719 Reorder the terms: -9.5 + x = 15.945218719 Solving -9.5 + x = 15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 15.945218719 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 15.945218719 + 9.5 x = 15.945218719 + 9.5 Combine like terms: 15.945218719 + 9.5 = 25.445218719 x = 25.445218719 Simplifying x = 25.445218719Subproblem 2
x + -9.5 = -15.945218719 Simplifying x + -9.5 = -15.945218719 Reorder the terms: -9.5 + x = -15.945218719 Solving -9.5 + x = -15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -15.945218719 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -15.945218719 + 9.5 x = -15.945218719 + 9.5 Combine like terms: -15.945218719 + 9.5 = -6.445218719 x = -6.445218719 Simplifying x = -6.445218719Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.445218719, -6.445218719}
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