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Simplifying -0.0005(x2 + -12000x + 800000) = 0 Reorder the terms: -0.0005(800000 + -12000x + x2) = 0 (800000 * -0.0005 + -12000x * -0.0005 + x2 * -0.0005) = 0 (-400 + 6x + -0.0005x2) = 0 Solving -400 + 6x + -0.0005x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0005 the coefficient of the squared term: Divide each side by '-0.0005'. 800000 + -12000x + x2 = 0 Move the constant term to the right: Add '-800000' to each side of the equation. 800000 + -12000x + -800000 + x2 = 0 + -800000 Reorder the terms: 800000 + -800000 + -12000x + x2 = 0 + -800000 Combine like terms: 800000 + -800000 = 0 0 + -12000x + x2 = 0 + -800000 -12000x + x2 = 0 + -800000 Combine like terms: 0 + -800000 = -800000 -12000x + x2 = -800000 The x term is -12000x. Take half its coefficient (-6000). Square it (36000000) and add it to both sides. Add '36000000' to each side of the equation. -12000x + 36000000 + x2 = -800000 + 36000000 Reorder the terms: 36000000 + -12000x + x2 = -800000 + 36000000 Combine like terms: -800000 + 36000000 = 35200000 36000000 + -12000x + x2 = 35200000 Factor a perfect square on the left side: (x + -6000)(x + -6000) = 35200000 Calculate the square root of the right side: 5932.958789677 Break this problem into two subproblems by setting (x + -6000) equal to 5932.958789677 and -5932.958789677.Subproblem 1
x + -6000 = 5932.958789677 Simplifying x + -6000 = 5932.958789677 Reorder the terms: -6000 + x = 5932.958789677 Solving -6000 + x = 5932.958789677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + 6000 + x = 5932.958789677 + 6000 Combine like terms: -6000 + 6000 = 0 0 + x = 5932.958789677 + 6000 x = 5932.958789677 + 6000 Combine like terms: 5932.958789677 + 6000 = 11932.958789677 x = 11932.958789677 Simplifying x = 11932.958789677Subproblem 2
x + -6000 = -5932.958789677 Simplifying x + -6000 = -5932.958789677 Reorder the terms: -6000 + x = -5932.958789677 Solving -6000 + x = -5932.958789677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + 6000 + x = -5932.958789677 + 6000 Combine like terms: -6000 + 6000 = 0 0 + x = -5932.958789677 + 6000 x = -5932.958789677 + 6000 Combine like terms: -5932.958789677 + 6000 = 67.041210323 x = 67.041210323 Simplifying x = 67.041210323Solution
The solution to the problem is based on the solutions from the subproblems. x = {11932.958789677, 67.041210323}
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