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Simplifying 96000 = 2731x2 + 5951x + 5756 Reorder the terms: 96000 = 5756 + 5951x + 2731x2 Solving 96000 = 5756 + 5951x + 2731x2 Solving for variable 'x'. Combine like terms: 96000 + -5756 = 90244 90244 + -5951x + -2731x2 = 5756 + 5951x + 2731x2 + -5756 + -5951x + -2731x2 Reorder the terms: 90244 + -5951x + -2731x2 = 5756 + -5756 + 5951x + -5951x + 2731x2 + -2731x2 Combine like terms: 5756 + -5756 = 0 90244 + -5951x + -2731x2 = 0 + 5951x + -5951x + 2731x2 + -2731x2 90244 + -5951x + -2731x2 = 5951x + -5951x + 2731x2 + -2731x2 Combine like terms: 5951x + -5951x = 0 90244 + -5951x + -2731x2 = 0 + 2731x2 + -2731x2 90244 + -5951x + -2731x2 = 2731x2 + -2731x2 Combine like terms: 2731x2 + -2731x2 = 0 90244 + -5951x + -2731x2 = 0 Begin completing the square. Divide all terms by -2731 the coefficient of the squared term: Divide each side by '-2731'. -33.04430611 + 2.179055291x + x2 = 0 Move the constant term to the right: Add '33.04430611' to each side of the equation. -33.04430611 + 2.179055291x + 33.04430611 + x2 = 0 + 33.04430611 Reorder the terms: -33.04430611 + 33.04430611 + 2.179055291x + x2 = 0 + 33.04430611 Combine like terms: -33.04430611 + 33.04430611 = 0.00000000 0.00000000 + 2.179055291x + x2 = 0 + 33.04430611 2.179055291x + x2 = 0 + 33.04430611 Combine like terms: 0 + 33.04430611 = 33.04430611 2.179055291x + x2 = 33.04430611 The x term is 2.179055291x. Take half its coefficient (1.089527646). Square it (1.187070491) and add it to both sides. Add '1.187070491' to each side of the equation. 2.179055291x + 1.187070491 + x2 = 33.04430611 + 1.187070491 Reorder the terms: 1.187070491 + 2.179055291x + x2 = 33.04430611 + 1.187070491 Combine like terms: 33.04430611 + 1.187070491 = 34.231376601 1.187070491 + 2.179055291x + x2 = 34.231376601 Factor a perfect square on the left side: (x + 1.089527646)(x + 1.089527646) = 34.231376601 Calculate the square root of the right side: 5.850758635 Break this problem into two subproblems by setting (x + 1.089527646) equal to 5.850758635 and -5.850758635.Subproblem 1
x + 1.089527646 = 5.850758635 Simplifying x + 1.089527646 = 5.850758635 Reorder the terms: 1.089527646 + x = 5.850758635 Solving 1.089527646 + x = 5.850758635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.089527646' to each side of the equation. 1.089527646 + -1.089527646 + x = 5.850758635 + -1.089527646 Combine like terms: 1.089527646 + -1.089527646 = 0.000000000 0.000000000 + x = 5.850758635 + -1.089527646 x = 5.850758635 + -1.089527646 Combine like terms: 5.850758635 + -1.089527646 = 4.761230989 x = 4.761230989 Simplifying x = 4.761230989Subproblem 2
x + 1.089527646 = -5.850758635 Simplifying x + 1.089527646 = -5.850758635 Reorder the terms: 1.089527646 + x = -5.850758635 Solving 1.089527646 + x = -5.850758635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.089527646' to each side of the equation. 1.089527646 + -1.089527646 + x = -5.850758635 + -1.089527646 Combine like terms: 1.089527646 + -1.089527646 = 0.000000000 0.000000000 + x = -5.850758635 + -1.089527646 x = -5.850758635 + -1.089527646 Combine like terms: -5.850758635 + -1.089527646 = -6.940286281 x = -6.940286281 Simplifying x = -6.940286281Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.761230989, -6.940286281}
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