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Simplifying 144.17 + -33.66x + x2 = 0 Solving 144.17 + -33.66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-144.17' to each side of the equation. 144.17 + -33.66x + -144.17 + x2 = 0 + -144.17 Reorder the terms: 144.17 + -144.17 + -33.66x + x2 = 0 + -144.17 Combine like terms: 144.17 + -144.17 = 0.00 0.00 + -33.66x + x2 = 0 + -144.17 -33.66x + x2 = 0 + -144.17 Combine like terms: 0 + -144.17 = -144.17 -33.66x + x2 = -144.17 The x term is -33.66x. Take half its coefficient (-16.83). Square it (283.2489) and add it to both sides. Add '283.2489' to each side of the equation. -33.66x + 283.2489 + x2 = -144.17 + 283.2489 Reorder the terms: 283.2489 + -33.66x + x2 = -144.17 + 283.2489 Combine like terms: -144.17 + 283.2489 = 139.0789 283.2489 + -33.66x + x2 = 139.0789 Factor a perfect square on the left side: (x + -16.83)(x + -16.83) = 139.0789 Calculate the square root of the right side: 11.793171753 Break this problem into two subproblems by setting (x + -16.83) equal to 11.793171753 and -11.793171753.Subproblem 1
x + -16.83 = 11.793171753 Simplifying x + -16.83 = 11.793171753 Reorder the terms: -16.83 + x = 11.793171753 Solving -16.83 + x = 11.793171753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.83' to each side of the equation. -16.83 + 16.83 + x = 11.793171753 + 16.83 Combine like terms: -16.83 + 16.83 = 0.00 0.00 + x = 11.793171753 + 16.83 x = 11.793171753 + 16.83 Combine like terms: 11.793171753 + 16.83 = 28.623171753 x = 28.623171753 Simplifying x = 28.623171753Subproblem 2
x + -16.83 = -11.793171753 Simplifying x + -16.83 = -11.793171753 Reorder the terms: -16.83 + x = -11.793171753 Solving -16.83 + x = -11.793171753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.83' to each side of the equation. -16.83 + 16.83 + x = -11.793171753 + 16.83 Combine like terms: -16.83 + 16.83 = 0.00 0.00 + x = -11.793171753 + 16.83 x = -11.793171753 + 16.83 Combine like terms: -11.793171753 + 16.83 = 5.036828247 x = 5.036828247 Simplifying x = 5.036828247Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.623171753, 5.036828247}
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