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Simplifying 2x2 + -55x + 15 = 122 Reorder the terms: 15 + -55x + 2x2 = 122 Solving 15 + -55x + 2x2 = 122 Solving for variable 'x'. Reorder the terms: 15 + -122 + -55x + 2x2 = 122 + -122 Combine like terms: 15 + -122 = -107 -107 + -55x + 2x2 = 122 + -122 Combine like terms: 122 + -122 = 0 -107 + -55x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -53.5 + -27.5x + x2 = 0 Move the constant term to the right: Add '53.5' to each side of the equation. -53.5 + -27.5x + 53.5 + x2 = 0 + 53.5 Reorder the terms: -53.5 + 53.5 + -27.5x + x2 = 0 + 53.5 Combine like terms: -53.5 + 53.5 = 0.0 0.0 + -27.5x + x2 = 0 + 53.5 -27.5x + x2 = 0 + 53.5 Combine like terms: 0 + 53.5 = 53.5 -27.5x + x2 = 53.5 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 = 53.5 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = 53.5 + 189.0625 Combine like terms: 53.5 + 189.0625 = 242.5625 189.0625 + -27.5x + x2 = 242.5625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 242.5625 Calculate the square root of the right side: 15.574418127 Break this problem into two subproblems by setting (x + -13.75) equal to 15.574418127 and -15.574418127.Subproblem 1
x + -13.75 = 15.574418127 Simplifying x + -13.75 = 15.574418127 Reorder the terms: -13.75 + x = 15.574418127 Solving -13.75 + x = 15.574418127 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 = 15.574418127 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 15.574418127 + 13.75 x = 15.574418127 + 13.75 Combine like terms: 15.574418127 + 13.75 = 29.324418127 x = 29.324418127 Simplifying x = 29.324418127Subproblem 2
x + -13.75 = -15.574418127 Simplifying x + -13.75 = -15.574418127 Reorder the terms: -13.75 + x = -15.574418127 Solving -13.75 + x = -15.574418127 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 = -15.574418127 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -15.574418127 + 13.75 x = -15.574418127 + 13.75 Combine like terms: -15.574418127 + 13.75 = -1.824418127 x = -1.824418127 Simplifying x = -1.824418127Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.324418127, -1.824418127}
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