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Simplifying -0.0005x2 + 45x = 1000000 Reorder the terms: 45x + -0.0005x2 = 1000000 Solving 45x + -0.0005x2 = 1000000 Solving for variable 'x'. Reorder the terms: -1000000 + 45x + -0.0005x2 = 1000000 + -1000000 Combine like terms: 1000000 + -1000000 = 0 -1000000 + 45x + -0.0005x2 = 0 Begin completing the square. Divide all terms by -0.0005 the coefficient of the squared term: Divide each side by '-0.0005'. 2000000000 + -90000x + x2 = 0 Move the constant term to the right: Add '-2000000000' to each side of the equation. 2000000000 + -90000x + -2000000000 + x2 = 0 + -2000000000 Reorder the terms: 2000000000 + -2000000000 + -90000x + x2 = 0 + -2000000000 Combine like terms: 2000000000 + -2000000000 = 0 0 + -90000x + x2 = 0 + -2000000000 -90000x + x2 = 0 + -2000000000 Combine like terms: 0 + -2000000000 = -2000000000 -90000x + x2 = -2000000000 The x term is -90000x. Take half its coefficient (-45000). Square it (2025000000) and add it to both sides. Add '2025000000' to each side of the equation. -90000x + 2025000000 + x2 = -2000000000 + 2025000000 Reorder the terms: 2025000000 + -90000x + x2 = -2000000000 + 2025000000 Combine like terms: -2000000000 + 2025000000 = 25000000 2025000000 + -90000x + x2 = 25000000 Factor a perfect square on the left side: (x + -45000)(x + -45000) = 25000000 Calculate the square root of the right side: 5000 Break this problem into two subproblems by setting (x + -45000) equal to 5000 and -5000.Subproblem 1
x + -45000 = 5000 Simplifying x + -45000 = 5000 Reorder the terms: -45000 + x = 5000 Solving -45000 + x = 5000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45000' to each side of the equation. -45000 + 45000 + x = 5000 + 45000 Combine like terms: -45000 + 45000 = 0 0 + x = 5000 + 45000 x = 5000 + 45000 Combine like terms: 5000 + 45000 = 50000 x = 50000 Simplifying x = 50000Subproblem 2
x + -45000 = -5000 Simplifying x + -45000 = -5000 Reorder the terms: -45000 + x = -5000 Solving -45000 + x = -5000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45000' to each side of the equation. -45000 + 45000 + x = -5000 + 45000 Combine like terms: -45000 + 45000 = 0 0 + x = -5000 + 45000 x = -5000 + 45000 Combine like terms: -5000 + 45000 = 40000 x = 40000 Simplifying x = 40000Solution
The solution to the problem is based on the solutions from the subproblems. x = {50000, 40000}
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