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Simplifying 1000000 = -1x2 + 3000x Reorder the terms: 1000000 = 3000x + -1x2 Solving 1000000 = 3000x + -1x2 Solving for variable 'x'. Reorder the terms: 1000000 + -3000x + x2 = 3000x + -3000x + -1x2 + x2 Combine like terms: 3000x + -3000x = 0 1000000 + -3000x + x2 = 0 + -1x2 + x2 1000000 + -3000x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1000000 + -3000x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1000000' to each side of the equation. 1000000 + -3000x + -1000000 + x2 = 0 + -1000000 Reorder the terms: 1000000 + -1000000 + -3000x + x2 = 0 + -1000000 Combine like terms: 1000000 + -1000000 = 0 0 + -3000x + x2 = 0 + -1000000 -3000x + x2 = 0 + -1000000 Combine like terms: 0 + -1000000 = -1000000 -3000x + x2 = -1000000 The x term is -3000x. Take half its coefficient (-1500). Square it (2250000) and add it to both sides. Add '2250000' to each side of the equation. -3000x + 2250000 + x2 = -1000000 + 2250000 Reorder the terms: 2250000 + -3000x + x2 = -1000000 + 2250000 Combine like terms: -1000000 + 2250000 = 1250000 2250000 + -3000x + x2 = 1250000 Factor a perfect square on the left side: (x + -1500)(x + -1500) = 1250000 Calculate the square root of the right side: 1118.03398875 Break this problem into two subproblems by setting (x + -1500) equal to 1118.03398875 and -1118.03398875.Subproblem 1
x + -1500 = 1118.03398875 Simplifying x + -1500 = 1118.03398875 Reorder the terms: -1500 + x = 1118.03398875 Solving -1500 + x = 1118.03398875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1500' to each side of the equation. -1500 + 1500 + x = 1118.03398875 + 1500 Combine like terms: -1500 + 1500 = 0 0 + x = 1118.03398875 + 1500 x = 1118.03398875 + 1500 Combine like terms: 1118.03398875 + 1500 = 2618.03398875 x = 2618.03398875 Simplifying x = 2618.03398875Subproblem 2
x + -1500 = -1118.03398875 Simplifying x + -1500 = -1118.03398875 Reorder the terms: -1500 + x = -1118.03398875 Solving -1500 + x = -1118.03398875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1500' to each side of the equation. -1500 + 1500 + x = -1118.03398875 + 1500 Combine like terms: -1500 + 1500 = 0 0 + x = -1118.03398875 + 1500 x = -1118.03398875 + 1500 Combine like terms: -1118.03398875 + 1500 = 381.96601125 x = 381.96601125 Simplifying x = 381.96601125Solution
The solution to the problem is based on the solutions from the subproblems. x = {2618.03398875, 381.96601125}
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