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Simplifying x2 + (170.868x) + -123024.96 = 0 Reorder the terms: -123024.96 + (170.868x) + x2 = 0 Solving -123024.96 + (170.868x) + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '123024.96' to each side of the equation. -123024.96 + (170.868x) + 123024.96 + x2 = 0 + 123024.96 Reorder the terms: -123024.96 + 123024.96 + (170.868x) + x2 = 0 + 123024.96 Combine like terms: -123024.96 + 123024.96 = 0.00 0.00 + (170.868x) + x2 = 0 + 123024.96 (170.868x) + x2 = 0 + 123024.96 Combine like terms: 0 + 123024.96 = 123024.96 (170.868x) + x2 = 123024.96 The x term is (170.868x). Take half its coefficient (85.434). Square it (7298.968356) and add it to both sides. Add '7298.968356' to each side of the equation. (170.868x) + 7298.968356 + x2 = 123024.96 + 7298.968356 Reorder the terms: 7298.968356 + (170.868x) + x2 = 123024.96 + 7298.968356 Combine like terms: 123024.96 + 7298.968356 = 130323.928356 7298.968356 + (170.868x) + x2 = 130323.928356 Factor a perfect square on the left side: (x + 85.434)(x + 85.434) = 130323.928356 Calculate the square root of the right side: 361.004055872 Break this problem into two subproblems by setting (x + 85.434) equal to 361.004055872 and -361.004055872.Subproblem 1
x + 85.434 = 361.004055872 Simplifying x + 85.434 = 361.004055872 Reorder the terms: 85.434 + x = 361.004055872 Solving 85.434 + x = 361.004055872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-85.434' to each side of the equation. 85.434 + -85.434 + x = 361.004055872 + -85.434 Combine like terms: 85.434 + -85.434 = 0.000 0.000 + x = 361.004055872 + -85.434 x = 361.004055872 + -85.434 Combine like terms: 361.004055872 + -85.434 = 275.570055872 x = 275.570055872 Simplifying x = 275.570055872Subproblem 2
x + 85.434 = -361.004055872 Simplifying x + 85.434 = -361.004055872 Reorder the terms: 85.434 + x = -361.004055872 Solving 85.434 + x = -361.004055872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-85.434' to each side of the equation. 85.434 + -85.434 + x = -361.004055872 + -85.434 Combine like terms: 85.434 + -85.434 = 0.000 0.000 + x = -361.004055872 + -85.434 x = -361.004055872 + -85.434 Combine like terms: -361.004055872 + -85.434 = -446.438055872 x = -446.438055872 Simplifying x = -446.438055872Solution
The solution to the problem is based on the solutions from the subproblems. x = {275.570055872, -446.438055872}
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