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Simplifying -1.592x2 + 39.360x + 384.134 = 0 Reorder the terms: 384.134 + 39.360x + -1.592x2 = 0 Solving 384.134 + 39.360x + -1.592x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.592 the coefficient of the squared term: Divide each side by '-1.592'. -241.290201 + -24.72361809x + x2 = 0 Move the constant term to the right: Add '241.290201' to each side of the equation. -241.290201 + -24.72361809x + 241.290201 + x2 = 0 + 241.290201 Reorder the terms: -241.290201 + 241.290201 + -24.72361809x + x2 = 0 + 241.290201 Combine like terms: -241.290201 + 241.290201 = 0.000000 0.000000 + -24.72361809x + x2 = 0 + 241.290201 -24.72361809x + x2 = 0 + 241.290201 Combine like terms: 0 + 241.290201 = 241.290201 -24.72361809x + x2 = 241.290201 The x term is -24.72361809x. Take half its coefficient (-12.36180905). Square it (152.8143230) and add it to both sides. Add '152.8143230' to each side of the equation. -24.72361809x + 152.8143230 + x2 = 241.290201 + 152.8143230 Reorder the terms: 152.8143230 + -24.72361809x + x2 = 241.290201 + 152.8143230 Combine like terms: 241.290201 + 152.8143230 = 394.104524 152.8143230 + -24.72361809x + x2 = 394.104524 Factor a perfect square on the left side: (x + -12.36180905)(x + -12.36180905) = 394.104524 Calculate the square root of the right side: 19.852065988 Break this problem into two subproblems by setting (x + -12.36180905) equal to 19.852065988 and -19.852065988.Subproblem 1
x + -12.36180905 = 19.852065988 Simplifying x + -12.36180905 = 19.852065988 Reorder the terms: -12.36180905 + x = 19.852065988 Solving -12.36180905 + x = 19.852065988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.36180905' to each side of the equation. -12.36180905 + 12.36180905 + x = 19.852065988 + 12.36180905 Combine like terms: -12.36180905 + 12.36180905 = 0.00000000 0.00000000 + x = 19.852065988 + 12.36180905 x = 19.852065988 + 12.36180905 Combine like terms: 19.852065988 + 12.36180905 = 32.213875038 x = 32.213875038 Simplifying x = 32.213875038Subproblem 2
x + -12.36180905 = -19.852065988 Simplifying x + -12.36180905 = -19.852065988 Reorder the terms: -12.36180905 + x = -19.852065988 Solving -12.36180905 + x = -19.852065988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.36180905' to each side of the equation. -12.36180905 + 12.36180905 + x = -19.852065988 + 12.36180905 Combine like terms: -12.36180905 + 12.36180905 = 0.00000000 0.00000000 + x = -19.852065988 + 12.36180905 x = -19.852065988 + 12.36180905 Combine like terms: -19.852065988 + 12.36180905 = -7.490256938 x = -7.490256938 Simplifying x = -7.490256938Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.213875038, -7.490256938}
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