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Simplifying 3x2 + 125x + -4000 = 0 Reorder the terms: -4000 + 125x + 3x2 = 0 Solving -4000 + 125x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1333.333333 + 41.66666667x + x2 = 0 Move the constant term to the right: Add '1333.333333' to each side of the equation. -1333.333333 + 41.66666667x + 1333.333333 + x2 = 0 + 1333.333333 Reorder the terms: -1333.333333 + 1333.333333 + 41.66666667x + x2 = 0 + 1333.333333 Combine like terms: -1333.333333 + 1333.333333 = 0.000000 0.000000 + 41.66666667x + x2 = 0 + 1333.333333 41.66666667x + x2 = 0 + 1333.333333 Combine like terms: 0 + 1333.333333 = 1333.333333 41.66666667x + x2 = 1333.333333 The x term is 41.66666667x. Take half its coefficient (20.83333334). Square it (434.0277781) and add it to both sides. Add '434.0277781' to each side of the equation. 41.66666667x + 434.0277781 + x2 = 1333.333333 + 434.0277781 Reorder the terms: 434.0277781 + 41.66666667x + x2 = 1333.333333 + 434.0277781 Combine like terms: 1333.333333 + 434.0277781 = 1767.3611111 434.0277781 + 41.66666667x + x2 = 1767.3611111 Factor a perfect square on the left side: (x + 20.83333334)(x + 20.83333334) = 1767.3611111 Calculate the square root of the right side: 42.039994185 Break this problem into two subproblems by setting (x + 20.83333334) equal to 42.039994185 and -42.039994185.Subproblem 1
x + 20.83333334 = 42.039994185 Simplifying x + 20.83333334 = 42.039994185 Reorder the terms: 20.83333334 + x = 42.039994185 Solving 20.83333334 + x = 42.039994185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.83333334' to each side of the equation. 20.83333334 + -20.83333334 + x = 42.039994185 + -20.83333334 Combine like terms: 20.83333334 + -20.83333334 = 0.00000000 0.00000000 + x = 42.039994185 + -20.83333334 x = 42.039994185 + -20.83333334 Combine like terms: 42.039994185 + -20.83333334 = 21.206660845 x = 21.206660845 Simplifying x = 21.206660845Subproblem 2
x + 20.83333334 = -42.039994185 Simplifying x + 20.83333334 = -42.039994185 Reorder the terms: 20.83333334 + x = -42.039994185 Solving 20.83333334 + x = -42.039994185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.83333334' to each side of the equation. 20.83333334 + -20.83333334 + x = -42.039994185 + -20.83333334 Combine like terms: 20.83333334 + -20.83333334 = 0.00000000 0.00000000 + x = -42.039994185 + -20.83333334 x = -42.039994185 + -20.83333334 Combine like terms: -42.039994185 + -20.83333334 = -62.873327525 x = -62.873327525 Simplifying x = -62.873327525Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.206660845, -62.873327525}
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