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Simplifying x * x + -2x = 3x + 108 Multiply x * x x2 + -2x = 3x + 108 Reorder the terms: -2x + x2 = 3x + 108 Reorder the terms: -2x + x2 = 108 + 3x Solving -2x + x2 = 108 + 3x Solving for variable 'x'. Reorder the terms: -108 + -2x + -3x + x2 = 108 + 3x + -108 + -3x Combine like terms: -2x + -3x = -5x -108 + -5x + x2 = 108 + 3x + -108 + -3x Reorder the terms: -108 + -5x + x2 = 108 + -108 + 3x + -3x Combine like terms: 108 + -108 = 0 -108 + -5x + x2 = 0 + 3x + -3x -108 + -5x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -108 + -5x + x2 = 0 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 = 13.188779163 x = 13.188779163 Simplifying x = 13.188779163Subproblem 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 = -8.188779163 x = -8.188779163 Simplifying x = -8.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.188779163, -8.188779163}
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