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Simplifying 2000x2 + 2100x + -4601 = 0 Reorder the terms: -4601 + 2100x + 2000x2 = 0 Solving -4601 + 2100x + 2000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2000 the coefficient of the squared term: Divide each side by '2000'. -2.3005 + 1.05x + x2 = 0 Move the constant term to the right: Add '2.3005' to each side of the equation. -2.3005 + 1.05x + 2.3005 + x2 = 0 + 2.3005 Reorder the terms: -2.3005 + 2.3005 + 1.05x + x2 = 0 + 2.3005 Combine like terms: -2.3005 + 2.3005 = 0.0000 0.0000 + 1.05x + x2 = 0 + 2.3005 1.05x + x2 = 0 + 2.3005 Combine like terms: 0 + 2.3005 = 2.3005 1.05x + x2 = 2.3005 The x term is 1.05x. Take half its coefficient (0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. 1.05x + 0.275625 + x2 = 2.3005 + 0.275625 Reorder the terms: 0.275625 + 1.05x + x2 = 2.3005 + 0.275625 Combine like terms: 2.3005 + 0.275625 = 2.576125 0.275625 + 1.05x + x2 = 2.576125 Factor a perfect square on the left side: (x + 0.525)(x + 0.525) = 2.576125 Calculate the square root of the right side: 1.605031152 Break this problem into two subproblems by setting (x + 0.525) equal to 1.605031152 and -1.605031152.Subproblem 1
x + 0.525 = 1.605031152 Simplifying x + 0.525 = 1.605031152 Reorder the terms: 0.525 + x = 1.605031152 Solving 0.525 + x = 1.605031152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = 1.605031152 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = 1.605031152 + -0.525 x = 1.605031152 + -0.525 Combine like terms: 1.605031152 + -0.525 = 1.080031152 x = 1.080031152 Simplifying x = 1.080031152Subproblem 2
x + 0.525 = -1.605031152 Simplifying x + 0.525 = -1.605031152 Reorder the terms: 0.525 + x = -1.605031152 Solving 0.525 + x = -1.605031152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = -1.605031152 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = -1.605031152 + -0.525 x = -1.605031152 + -0.525 Combine like terms: -1.605031152 + -0.525 = -2.130031152 x = -2.130031152 Simplifying x = -2.130031152Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.080031152, -2.130031152}
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