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Simplifying 0.001x(x + -5) = 750 Reorder the terms: 0.001x(-5 + x) = 750 (-5 * 0.001x + x * 0.001x) = 750 (-0.005x + 0.001x2) = 750 Solving -0.005x + 0.001x2 = 750 Solving for variable 'x'. Reorder the terms: -750 + -0.005x + 0.001x2 = 750 + -750 Combine like terms: 750 + -750 = 0 -750 + -0.005x + 0.001x2 = 0 Begin completing the square. Divide all terms by 0.001 the coefficient of the squared term: Divide each side by '0.001'. -750000 + -5x + x2 = 0 Move the constant term to the right: Add '750000' to each side of the equation. -750000 + -5x + 750000 + x2 = 0 + 750000 Reorder the terms: -750000 + 750000 + -5x + x2 = 0 + 750000 Combine like terms: -750000 + 750000 = 0 0 + -5x + x2 = 0 + 750000 -5x + x2 = 0 + 750000 Combine like terms: 0 + 750000 = 750000 -5x + x2 = 750000 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 750000 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 750000 + 6.25 Combine like terms: 750000 + 6.25 = 750006.25 6.25 + -5x + x2 = 750006.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 750006.25 Calculate the square root of the right side: 866.029012216 Break this problem into two subproblems by setting (x + -2.5) equal to 866.029012216 and -866.029012216.Subproblem 1
x + -2.5 = 866.029012216 Simplifying x + -2.5 = 866.029012216 Reorder the terms: -2.5 + x = 866.029012216 Solving -2.5 + x = 866.029012216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 866.029012216 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 866.029012216 + 2.5 x = 866.029012216 + 2.5 Combine like terms: 866.029012216 + 2.5 = 868.529012216 x = 868.529012216 Simplifying x = 868.529012216Subproblem 2
x + -2.5 = -866.029012216 Simplifying x + -2.5 = -866.029012216 Reorder the terms: -2.5 + x = -866.029012216 Solving -2.5 + x = -866.029012216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -866.029012216 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -866.029012216 + 2.5 x = -866.029012216 + 2.5 Combine like terms: -866.029012216 + 2.5 = -863.529012216 x = -863.529012216 Simplifying x = -863.529012216Solution
The solution to the problem is based on the solutions from the subproblems. x = {868.529012216, -863.529012216}
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