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Simplifying -0.0025x2 + 12x + -4400 = 0 Reorder the terms: -4400 + 12x + -0.0025x2 = 0 Solving -4400 + 12x + -0.0025x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0025 the coefficient of the squared term: Divide each side by '-0.0025'. 1760000 + -4800x + x2 = 0 Move the constant term to the right: Add '-1760000' to each side of the equation. 1760000 + -4800x + -1760000 + x2 = 0 + -1760000 Reorder the terms: 1760000 + -1760000 + -4800x + x2 = 0 + -1760000 Combine like terms: 1760000 + -1760000 = 0 0 + -4800x + x2 = 0 + -1760000 -4800x + x2 = 0 + -1760000 Combine like terms: 0 + -1760000 = -1760000 -4800x + x2 = -1760000 The x term is -4800x. Take half its coefficient (-2400). Square it (5760000) and add it to both sides. Add '5760000' to each side of the equation. -4800x + 5760000 + x2 = -1760000 + 5760000 Reorder the terms: 5760000 + -4800x + x2 = -1760000 + 5760000 Combine like terms: -1760000 + 5760000 = 4000000 5760000 + -4800x + x2 = 4000000 Factor a perfect square on the left side: (x + -2400)(x + -2400) = 4000000 Calculate the square root of the right side: 2000 Break this problem into two subproblems by setting (x + -2400) equal to 2000 and -2000.Subproblem 1
x + -2400 = 2000 Simplifying x + -2400 = 2000 Reorder the terms: -2400 + x = 2000 Solving -2400 + x = 2000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2400' to each side of the equation. -2400 + 2400 + x = 2000 + 2400 Combine like terms: -2400 + 2400 = 0 0 + x = 2000 + 2400 x = 2000 + 2400 Combine like terms: 2000 + 2400 = 4400 x = 4400 Simplifying x = 4400Subproblem 2
x + -2400 = -2000 Simplifying x + -2400 = -2000 Reorder the terms: -2400 + x = -2000 Solving -2400 + x = -2000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2400' to each side of the equation. -2400 + 2400 + x = -2000 + 2400 Combine like terms: -2400 + 2400 = 0 0 + x = -2000 + 2400 x = -2000 + 2400 Combine like terms: -2000 + 2400 = 400 x = 400 Simplifying x = 400Solution
The solution to the problem is based on the solutions from the subproblems. x = {4400, 400}
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