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Simplifying 22x(11x + 4) = 840 Reorder the terms: 22x(4 + 11x) = 840 (4 * 22x + 11x * 22x) = 840 (88x + 242x2) = 840 Solving 88x + 242x2 = 840 Solving for variable 'x'. Reorder the terms: -840 + 88x + 242x2 = 840 + -840 Combine like terms: 840 + -840 = 0 -840 + 88x + 242x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-420 + 44x + 121x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-420 + 44x + 121x2)' equal to zero and attempt to solve: Simplifying -420 + 44x + 121x2 = 0 Solving -420 + 44x + 121x2 = 0 Begin completing the square. Divide all terms by 121 the coefficient of the squared term: Divide each side by '121'. -3.47107438 + 0.3636363636x + x2 = 0 Move the constant term to the right: Add '3.47107438' to each side of the equation. -3.47107438 + 0.3636363636x + 3.47107438 + x2 = 0 + 3.47107438 Reorder the terms: -3.47107438 + 3.47107438 + 0.3636363636x + x2 = 0 + 3.47107438 Combine like terms: -3.47107438 + 3.47107438 = 0.00000000 0.00000000 + 0.3636363636x + x2 = 0 + 3.47107438 0.3636363636x + x2 = 0 + 3.47107438 Combine like terms: 0 + 3.47107438 = 3.47107438 0.3636363636x + x2 = 3.47107438 The x term is 0.3636363636x. Take half its coefficient (0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. 0.3636363636x + 0.03305785123 + x2 = 3.47107438 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636x + x2 = 3.47107438 + 0.03305785123 Combine like terms: 3.47107438 + 0.03305785123 = 3.50413223123 0.03305785123 + 0.3636363636x + x2 = 3.50413223123 Factor a perfect square on the left side: (x + 0.1818181818)(x + 0.1818181818) = 3.50413223123 Calculate the square root of the right side: 1.871932753 Break this problem into two subproblems by setting (x + 0.1818181818) equal to 1.871932753 and -1.871932753.Subproblem 1
x + 0.1818181818 = 1.871932753 Simplifying x + 0.1818181818 = 1.871932753 Reorder the terms: 0.1818181818 + x = 1.871932753 Solving 0.1818181818 + x = 1.871932753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = 1.871932753 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 1.871932753 + -0.1818181818 x = 1.871932753 + -0.1818181818 Combine like terms: 1.871932753 + -0.1818181818 = 1.6901145712 x = 1.6901145712 Simplifying x = 1.6901145712Subproblem 2
x + 0.1818181818 = -1.871932753 Simplifying x + 0.1818181818 = -1.871932753 Reorder the terms: 0.1818181818 + x = -1.871932753 Solving 0.1818181818 + x = -1.871932753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = -1.871932753 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -1.871932753 + -0.1818181818 x = -1.871932753 + -0.1818181818 Combine like terms: -1.871932753 + -0.1818181818 = -2.0537509348 x = -2.0537509348 Simplifying x = -2.0537509348Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6901145712, -2.0537509348}Solution
x = {1.6901145712, -2.0537509348}
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