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Simplifying -0.032x2 + 42x + -3000 = 0 Reorder the terms: -3000 + 42x + -0.032x2 = 0 Solving -3000 + 42x + -0.032x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.032 the coefficient of the squared term: Divide each side by '-0.032'. 93750 + -1312.5x + x2 = 0 Move the constant term to the right: Add '-93750' to each side of the equation. 93750 + -1312.5x + -93750 + x2 = 0 + -93750 Reorder the terms: 93750 + -93750 + -1312.5x + x2 = 0 + -93750 Combine like terms: 93750 + -93750 = 0 0 + -1312.5x + x2 = 0 + -93750 -1312.5x + x2 = 0 + -93750 Combine like terms: 0 + -93750 = -93750 -1312.5x + x2 = -93750 The x term is -1312.5x. Take half its coefficient (-656.25). Square it (430664.0625) and add it to both sides. Add '430664.0625' to each side of the equation. -1312.5x + 430664.0625 + x2 = -93750 + 430664.0625 Reorder the terms: 430664.0625 + -1312.5x + x2 = -93750 + 430664.0625 Combine like terms: -93750 + 430664.0625 = 336914.0625 430664.0625 + -1312.5x + x2 = 336914.0625 Factor a perfect square on the left side: (x + -656.25)(x + -656.25) = 336914.0625 Calculate the square root of the right side: 580.442988156 Break this problem into two subproblems by setting (x + -656.25) equal to 580.442988156 and -580.442988156.Subproblem 1
x + -656.25 = 580.442988156 Simplifying x + -656.25 = 580.442988156 Reorder the terms: -656.25 + x = 580.442988156 Solving -656.25 + x = 580.442988156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '656.25' to each side of the equation. -656.25 + 656.25 + x = 580.442988156 + 656.25 Combine like terms: -656.25 + 656.25 = 0.00 0.00 + x = 580.442988156 + 656.25 x = 580.442988156 + 656.25 Combine like terms: 580.442988156 + 656.25 = 1236.692988156 x = 1236.692988156 Simplifying x = 1236.692988156Subproblem 2
x + -656.25 = -580.442988156 Simplifying x + -656.25 = -580.442988156 Reorder the terms: -656.25 + x = -580.442988156 Solving -656.25 + x = -580.442988156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '656.25' to each side of the equation. -656.25 + 656.25 + x = -580.442988156 + 656.25 Combine like terms: -656.25 + 656.25 = 0.00 0.00 + x = -580.442988156 + 656.25 x = -580.442988156 + 656.25 Combine like terms: -580.442988156 + 656.25 = 75.807011844 x = 75.807011844 Simplifying x = 75.807011844Solution
The solution to the problem is based on the solutions from the subproblems. x = {1236.692988156, 75.807011844}
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