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Simplifying 1.2x + x2 = 175000 Solving 1.2x + x2 = 175000 Solving for variable 'x'. Reorder the terms: -175000 + 1.2x + x2 = 175000 + -175000 Combine like terms: 175000 + -175000 = 0 -175000 + 1.2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '175000' to each side of the equation. -175000 + 1.2x + 175000 + x2 = 0 + 175000 Reorder the terms: -175000 + 175000 + 1.2x + x2 = 0 + 175000 Combine like terms: -175000 + 175000 = 0 0 + 1.2x + x2 = 0 + 175000 1.2x + x2 = 0 + 175000 Combine like terms: 0 + 175000 = 175000 1.2x + x2 = 175000 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 175000 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 175000 + 0.36 Combine like terms: 175000 + 0.36 = 175000.36 0.36 + 1.2x + x2 = 175000.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 175000.36 Calculate the square root of the right side: 418.330443549 Break this problem into two subproblems by setting (x + 0.6) equal to 418.330443549 and -418.330443549.Subproblem 1
x + 0.6 = 418.330443549 Simplifying x + 0.6 = 418.330443549 Reorder the terms: 0.6 + x = 418.330443549 Solving 0.6 + x = 418.330443549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 418.330443549 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 418.330443549 + -0.6 x = 418.330443549 + -0.6 Combine like terms: 418.330443549 + -0.6 = 417.730443549 x = 417.730443549 Simplifying x = 417.730443549Subproblem 2
x + 0.6 = -418.330443549 Simplifying x + 0.6 = -418.330443549 Reorder the terms: 0.6 + x = -418.330443549 Solving 0.6 + x = -418.330443549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -418.330443549 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -418.330443549 + -0.6 x = -418.330443549 + -0.6 Combine like terms: -418.330443549 + -0.6 = -418.930443549 x = -418.930443549 Simplifying x = -418.930443549Solution
The solution to the problem is based on the solutions from the subproblems. x = {417.730443549, -418.930443549}
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