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Simplifying 91000 = 3701x2 + 5591x + 5582 Reorder the terms: 91000 = 5582 + 5591x + 3701x2 Solving 91000 = 5582 + 5591x + 3701x2 Solving for variable 'x'. Combine like terms: 91000 + -5582 = 85418 85418 + -5591x + -3701x2 = 5582 + 5591x + 3701x2 + -5582 + -5591x + -3701x2 Reorder the terms: 85418 + -5591x + -3701x2 = 5582 + -5582 + 5591x + -5591x + 3701x2 + -3701x2 Combine like terms: 5582 + -5582 = 0 85418 + -5591x + -3701x2 = 0 + 5591x + -5591x + 3701x2 + -3701x2 85418 + -5591x + -3701x2 = 5591x + -5591x + 3701x2 + -3701x2 Combine like terms: 5591x + -5591x = 0 85418 + -5591x + -3701x2 = 0 + 3701x2 + -3701x2 85418 + -5591x + -3701x2 = 3701x2 + -3701x2 Combine like terms: 3701x2 + -3701x2 = 0 85418 + -5591x + -3701x2 = 0 Begin completing the square. Divide all terms by -3701 the coefficient of the squared term: Divide each side by '-3701'. -23.07970819 + 1.510672791x + x2 = 0 Move the constant term to the right: Add '23.07970819' to each side of the equation. -23.07970819 + 1.510672791x + 23.07970819 + x2 = 0 + 23.07970819 Reorder the terms: -23.07970819 + 23.07970819 + 1.510672791x + x2 = 0 + 23.07970819 Combine like terms: -23.07970819 + 23.07970819 = 0.00000000 0.00000000 + 1.510672791x + x2 = 0 + 23.07970819 1.510672791x + x2 = 0 + 23.07970819 Combine like terms: 0 + 23.07970819 = 23.07970819 1.510672791x + x2 = 23.07970819 The x term is 1.510672791x. Take half its coefficient (0.7553363955). Square it (0.5705330704) and add it to both sides. Add '0.5705330704' to each side of the equation. 1.510672791x + 0.5705330704 + x2 = 23.07970819 + 0.5705330704 Reorder the terms: 0.5705330704 + 1.510672791x + x2 = 23.07970819 + 0.5705330704 Combine like terms: 23.07970819 + 0.5705330704 = 23.6502412604 0.5705330704 + 1.510672791x + x2 = 23.6502412604 Factor a perfect square on the left side: (x + 0.7553363955)(x + 0.7553363955) = 23.6502412604 Calculate the square root of the right side: 4.863151371 Break this problem into two subproblems by setting (x + 0.7553363955) equal to 4.863151371 and -4.863151371.Subproblem 1
x + 0.7553363955 = 4.863151371 Simplifying x + 0.7553363955 = 4.863151371 Reorder the terms: 0.7553363955 + x = 4.863151371 Solving 0.7553363955 + x = 4.863151371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7553363955' to each side of the equation. 0.7553363955 + -0.7553363955 + x = 4.863151371 + -0.7553363955 Combine like terms: 0.7553363955 + -0.7553363955 = 0.0000000000 0.0000000000 + x = 4.863151371 + -0.7553363955 x = 4.863151371 + -0.7553363955 Combine like terms: 4.863151371 + -0.7553363955 = 4.1078149755 x = 4.1078149755 Simplifying x = 4.1078149755Subproblem 2
x + 0.7553363955 = -4.863151371 Simplifying x + 0.7553363955 = -4.863151371 Reorder the terms: 0.7553363955 + x = -4.863151371 Solving 0.7553363955 + x = -4.863151371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7553363955' to each side of the equation. 0.7553363955 + -0.7553363955 + x = -4.863151371 + -0.7553363955 Combine like terms: 0.7553363955 + -0.7553363955 = 0.0000000000 0.0000000000 + x = -4.863151371 + -0.7553363955 x = -4.863151371 + -0.7553363955 Combine like terms: -4.863151371 + -0.7553363955 = -5.6184877665 x = -5.6184877665 Simplifying x = -5.6184877665Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1078149755, -5.6184877665}
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