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Simplifying -53286.6x2 + 1801087.1x + -10146123.8 = 0 Reorder the terms: -10146123.8 + 1801087.1x + -53286.6x2 = 0 Solving -10146123.8 + 1801087.1x + -53286.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -53286.6 the coefficient of the squared term: Divide each side by '-53286.6'. 190.4066651 + -33.80000038x + x2 = 0 Move the constant term to the right: Add '-190.4066651' to each side of the equation. 190.4066651 + -33.80000038x + -190.4066651 + x2 = 0 + -190.4066651 Reorder the terms: 190.4066651 + -190.4066651 + -33.80000038x + x2 = 0 + -190.4066651 Combine like terms: 190.4066651 + -190.4066651 = 0.0000000 0.0000000 + -33.80000038x + x2 = 0 + -190.4066651 -33.80000038x + x2 = 0 + -190.4066651 Combine like terms: 0 + -190.4066651 = -190.4066651 -33.80000038x + x2 = -190.4066651 The x term is -33.80000038x. Take half its coefficient (-16.90000019). Square it (285.6100064) and add it to both sides. Add '285.6100064' to each side of the equation. -33.80000038x + 285.6100064 + x2 = -190.4066651 + 285.6100064 Reorder the terms: 285.6100064 + -33.80000038x + x2 = -190.4066651 + 285.6100064 Combine like terms: -190.4066651 + 285.6100064 = 95.2033413 285.6100064 + -33.80000038x + x2 = 95.2033413 Factor a perfect square on the left side: (x + -16.90000019)(x + -16.90000019) = 95.2033413 Calculate the square root of the right side: 9.757219958 Break this problem into two subproblems by setting (x + -16.90000019) equal to 9.757219958 and -9.757219958.Subproblem 1
x + -16.90000019 = 9.757219958 Simplifying x + -16.90000019 = 9.757219958 Reorder the terms: -16.90000019 + x = 9.757219958 Solving -16.90000019 + x = 9.757219958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.90000019' to each side of the equation. -16.90000019 + 16.90000019 + x = 9.757219958 + 16.90000019 Combine like terms: -16.90000019 + 16.90000019 = 0.00000000 0.00000000 + x = 9.757219958 + 16.90000019 x = 9.757219958 + 16.90000019 Combine like terms: 9.757219958 + 16.90000019 = 26.657220148 x = 26.657220148 Simplifying x = 26.657220148Subproblem 2
x + -16.90000019 = -9.757219958 Simplifying x + -16.90000019 = -9.757219958 Reorder the terms: -16.90000019 + x = -9.757219958 Solving -16.90000019 + x = -9.757219958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.90000019' to each side of the equation. -16.90000019 + 16.90000019 + x = -9.757219958 + 16.90000019 Combine like terms: -16.90000019 + 16.90000019 = 0.00000000 0.00000000 + x = -9.757219958 + 16.90000019 x = -9.757219958 + 16.90000019 Combine like terms: -9.757219958 + 16.90000019 = 7.142780232 x = 7.142780232 Simplifying x = 7.142780232Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.657220148, 7.142780232}
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