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Simplifying 1.5x + x2 = 1500000 Solving 1.5x + x2 = 1500000 Solving for variable 'x'. Reorder the terms: -1500000 + 1.5x + x2 = 1500000 + -1500000 Combine like terms: 1500000 + -1500000 = 0 -1500000 + 1.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1500000' to each side of the equation. -1500000 + 1.5x + 1500000 + x2 = 0 + 1500000 Reorder the terms: -1500000 + 1500000 + 1.5x + x2 = 0 + 1500000 Combine like terms: -1500000 + 1500000 = 0 0 + 1.5x + x2 = 0 + 1500000 1.5x + x2 = 0 + 1500000 Combine like terms: 0 + 1500000 = 1500000 1.5x + x2 = 1500000 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 1500000 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1500000 + 0.5625 Combine like terms: 1500000 + 0.5625 = 1500000.5625 0.5625 + 1.5x + x2 = 1500000.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1500000.5625 Calculate the square root of the right side: 1224.745101031 Break this problem into two subproblems by setting (x + 0.75) equal to 1224.745101031 and -1224.745101031.Subproblem 1
x + 0.75 = 1224.745101031 Simplifying x + 0.75 = 1224.745101031 Reorder the terms: 0.75 + x = 1224.745101031 Solving 0.75 + x = 1224.745101031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1224.745101031 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1224.745101031 + -0.75 x = 1224.745101031 + -0.75 Combine like terms: 1224.745101031 + -0.75 = 1223.995101031 x = 1223.995101031 Simplifying x = 1223.995101031Subproblem 2
x + 0.75 = -1224.745101031 Simplifying x + 0.75 = -1224.745101031 Reorder the terms: 0.75 + x = -1224.745101031 Solving 0.75 + x = -1224.745101031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1224.745101031 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1224.745101031 + -0.75 x = -1224.745101031 + -0.75 Combine like terms: -1224.745101031 + -0.75 = -1225.495101031 x = -1225.495101031 Simplifying x = -1225.495101031Solution
The solution to the problem is based on the solutions from the subproblems. x = {1223.995101031, -1225.495101031}
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