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Simplifying x2 + 191x + -4932.92 = 0 Reorder the terms: -4932.92 + 191x + x2 = 0 Solving -4932.92 + 191x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4932.92' to each side of the equation. -4932.92 + 191x + 4932.92 + x2 = 0 + 4932.92 Reorder the terms: -4932.92 + 4932.92 + 191x + x2 = 0 + 4932.92 Combine like terms: -4932.92 + 4932.92 = 0.00 0.00 + 191x + x2 = 0 + 4932.92 191x + x2 = 0 + 4932.92 Combine like terms: 0 + 4932.92 = 4932.92 191x + x2 = 4932.92 The x term is 191x. Take half its coefficient (95.5). Square it (9120.25) and add it to both sides. Add '9120.25' to each side of the equation. 191x + 9120.25 + x2 = 4932.92 + 9120.25 Reorder the terms: 9120.25 + 191x + x2 = 4932.92 + 9120.25 Combine like terms: 4932.92 + 9120.25 = 14053.17 9120.25 + 191x + x2 = 14053.17 Factor a perfect square on the left side: (x + 95.5)(x + 95.5) = 14053.17 Calculate the square root of the right side: 118.546066995 Break this problem into two subproblems by setting (x + 95.5) equal to 118.546066995 and -118.546066995.Subproblem 1
x + 95.5 = 118.546066995 Simplifying x + 95.5 = 118.546066995 Reorder the terms: 95.5 + x = 118.546066995 Solving 95.5 + x = 118.546066995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95.5' to each side of the equation. 95.5 + -95.5 + x = 118.546066995 + -95.5 Combine like terms: 95.5 + -95.5 = 0.0 0.0 + x = 118.546066995 + -95.5 x = 118.546066995 + -95.5 Combine like terms: 118.546066995 + -95.5 = 23.046066995 x = 23.046066995 Simplifying x = 23.046066995Subproblem 2
x + 95.5 = -118.546066995 Simplifying x + 95.5 = -118.546066995 Reorder the terms: 95.5 + x = -118.546066995 Solving 95.5 + x = -118.546066995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95.5' to each side of the equation. 95.5 + -95.5 + x = -118.546066995 + -95.5 Combine like terms: 95.5 + -95.5 = 0.0 0.0 + x = -118.546066995 + -95.5 x = -118.546066995 + -95.5 Combine like terms: -118.546066995 + -95.5 = -214.046066995 x = -214.046066995 Simplifying x = -214.046066995Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.046066995, -214.046066995}
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