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Simplifying 5749x + 3657x + 5x(224 + -6x + 4 + 55 + -9) = 88x + 55 + -4x Reorder the terms: 5749x + 3657x + 5x(224 + 4 + 55 + -9 + -6x) = 88x + 55 + -4x Combine like terms: 224 + 4 = 228 5749x + 3657x + 5x(228 + 55 + -9 + -6x) = 88x + 55 + -4x Combine like terms: 228 + 55 = 283 5749x + 3657x + 5x(283 + -9 + -6x) = 88x + 55 + -4x Combine like terms: 283 + -9 = 274 5749x + 3657x + 5x(274 + -6x) = 88x + 55 + -4x 5749x + 3657x + (274 * 5x + -6x * 5x) = 88x + 55 + -4x 5749x + 3657x + (1370x + -30x2) = 88x + 55 + -4x Combine like terms: 5749x + 3657x = 9406x 9406x + 1370x + -30x2 = 88x + 55 + -4x Combine like terms: 9406x + 1370x = 10776x 10776x + -30x2 = 88x + 55 + -4x Reorder the terms: 10776x + -30x2 = 55 + 88x + -4x Combine like terms: 88x + -4x = 84x 10776x + -30x2 = 55 + 84x Solving 10776x + -30x2 = 55 + 84x Solving for variable 'x'. Reorder the terms: -55 + 10776x + -84x + -30x2 = 55 + 84x + -55 + -84x Combine like terms: 10776x + -84x = 10692x -55 + 10692x + -30x2 = 55 + 84x + -55 + -84x Reorder the terms: -55 + 10692x + -30x2 = 55 + -55 + 84x + -84x Combine like terms: 55 + -55 = 0 -55 + 10692x + -30x2 = 0 + 84x + -84x -55 + 10692x + -30x2 = 84x + -84x Combine like terms: 84x + -84x = 0 -55 + 10692x + -30x2 = 0 Begin completing the square. Divide all terms by -30 the coefficient of the squared term: Divide each side by '-30'. 1.833333333 + -356.4x + x2 = 0.0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -356.4x + -1.833333333 + x2 = 0.0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -356.4x + x2 = 0.0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -356.4x + x2 = 0.0 + -1.833333333 -356.4x + x2 = 0.0 + -1.833333333 Combine like terms: 0.0 + -1.833333333 = -1.833333333 -356.4x + x2 = -1.833333333 The x term is -356.4x. Take half its coefficient (-178.2). Square it (31755.24) and add it to both sides. Add '31755.24' to each side of the equation. -356.4x + 31755.24 + x2 = -1.833333333 + 31755.24 Reorder the terms: 31755.24 + -356.4x + x2 = -1.833333333 + 31755.24 Combine like terms: -1.833333333 + 31755.24 = 31753.406666667 31755.24 + -356.4x + x2 = 31753.406666667 Factor a perfect square on the left side: (x + -178.2)(x + -178.2) = 31753.406666667 Calculate the square root of the right side: 178.194855893 Break this problem into two subproblems by setting (x + -178.2) equal to 178.194855893 and -178.194855893.Subproblem 1
x + -178.2 = 178.194855893 Simplifying x + -178.2 = 178.194855893 Reorder the terms: -178.2 + x = 178.194855893 Solving -178.2 + x = 178.194855893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '178.2' to each side of the equation. -178.2 + 178.2 + x = 178.194855893 + 178.2 Combine like terms: -178.2 + 178.2 = 0.0 0.0 + x = 178.194855893 + 178.2 x = 178.194855893 + 178.2 Combine like terms: 178.194855893 + 178.2 = 356.394855893 x = 356.394855893 Simplifying x = 356.394855893Subproblem 2
x + -178.2 = -178.194855893 Simplifying x + -178.2 = -178.194855893 Reorder the terms: -178.2 + x = -178.194855893 Solving -178.2 + x = -178.194855893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '178.2' to each side of the equation. -178.2 + 178.2 + x = -178.194855893 + 178.2 Combine like terms: -178.2 + 178.2 = 0.0 0.0 + x = -178.194855893 + 178.2 x = -178.194855893 + 178.2 Combine like terms: -178.194855893 + 178.2 = 0.005144107 x = 0.005144107 Simplifying x = 0.005144107Solution
The solution to the problem is based on the solutions from the subproblems. x = {356.394855893, 0.005144107}
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