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Simplifying 2000000 = -1x2 + 15000x Reorder the terms: 2000000 = 15000x + -1x2 Solving 2000000 = 15000x + -1x2 Solving for variable 'x'. Reorder the terms: 2000000 + -15000x + x2 = 15000x + -15000x + -1x2 + x2 Combine like terms: 15000x + -15000x = 0 2000000 + -15000x + x2 = 0 + -1x2 + x2 2000000 + -15000x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 2000000 + -15000x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2000000' to each side of the equation. 2000000 + -15000x + -2000000 + x2 = 0 + -2000000 Reorder the terms: 2000000 + -2000000 + -15000x + x2 = 0 + -2000000 Combine like terms: 2000000 + -2000000 = 0 0 + -15000x + x2 = 0 + -2000000 -15000x + x2 = 0 + -2000000 Combine like terms: 0 + -2000000 = -2000000 -15000x + x2 = -2000000 The x term is -15000x. Take half its coefficient (-7500). Square it (56250000) and add it to both sides. Add '56250000' to each side of the equation. -15000x + 56250000 + x2 = -2000000 + 56250000 Reorder the terms: 56250000 + -15000x + x2 = -2000000 + 56250000 Combine like terms: -2000000 + 56250000 = 54250000 56250000 + -15000x + x2 = 54250000 Factor a perfect square on the left side: (x + -7500)(x + -7500) = 54250000 Calculate the square root of the right side: 7365.459931328 Break this problem into two subproblems by setting (x + -7500) equal to 7365.459931328 and -7365.459931328.Subproblem 1
x + -7500 = 7365.459931328 Simplifying x + -7500 = 7365.459931328 Reorder the terms: -7500 + x = 7365.459931328 Solving -7500 + x = 7365.459931328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7500' to each side of the equation. -7500 + 7500 + x = 7365.459931328 + 7500 Combine like terms: -7500 + 7500 = 0 0 + x = 7365.459931328 + 7500 x = 7365.459931328 + 7500 Combine like terms: 7365.459931328 + 7500 = 14865.459931328 x = 14865.459931328 Simplifying x = 14865.459931328Subproblem 2
x + -7500 = -7365.459931328 Simplifying x + -7500 = -7365.459931328 Reorder the terms: -7500 + x = -7365.459931328 Solving -7500 + x = -7365.459931328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7500' to each side of the equation. -7500 + 7500 + x = -7365.459931328 + 7500 Combine like terms: -7500 + 7500 = 0 0 + x = -7365.459931328 + 7500 x = -7365.459931328 + 7500 Combine like terms: -7365.459931328 + 7500 = 134.540068672 x = 134.540068672 Simplifying x = 134.540068672Solution
The solution to the problem is based on the solutions from the subproblems. x = {14865.459931328, 134.540068672}
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