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Simplifying 2x2 + 55x + 150 = 0 Reorder the terms: 150 + 55x + 2x2 = 0 Solving 150 + 55x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 75 + 27.5x + x2 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + 27.5x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + 27.5x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + 27.5x + x2 = 0 + -75 27.5x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 27.5x + x2 = -75 The x term is 27.5x. Take half its coefficient (13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. 27.5x + 189.0625 + x2 = -75 + 189.0625 Reorder the terms: 189.0625 + 27.5x + x2 = -75 + 189.0625 Combine like terms: -75 + 189.0625 = 114.0625 189.0625 + 27.5x + x2 = 114.0625 Factor a perfect square on the left side: (x + 13.75)(x + 13.75) = 114.0625 Calculate the square root of the right side: 10.680004682 Break this problem into two subproblems by setting (x + 13.75) equal to 10.680004682 and -10.680004682.Subproblem 1
x + 13.75 = 10.680004682 Simplifying x + 13.75 = 10.680004682 Reorder the terms: 13.75 + x = 10.680004682 Solving 13.75 + x = 10.680004682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = 10.680004682 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = 10.680004682 + -13.75 x = 10.680004682 + -13.75 Combine like terms: 10.680004682 + -13.75 = -3.069995318 x = -3.069995318 Simplifying x = -3.069995318Subproblem 2
x + 13.75 = -10.680004682 Simplifying x + 13.75 = -10.680004682 Reorder the terms: 13.75 + x = -10.680004682 Solving 13.75 + x = -10.680004682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = -10.680004682 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = -10.680004682 + -13.75 x = -10.680004682 + -13.75 Combine like terms: -10.680004682 + -13.75 = -24.430004682 x = -24.430004682 Simplifying x = -24.430004682Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.069995318, -24.430004682}
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