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Simplifying x2 + 0.75x + -0.394 = 0 Reorder the terms: -0.394 + 0.75x + x2 = 0 Solving -0.394 + 0.75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.394' to each side of the equation. -0.394 + 0.75x + 0.394 + x2 = 0 + 0.394 Reorder the terms: -0.394 + 0.394 + 0.75x + x2 = 0 + 0.394 Combine like terms: -0.394 + 0.394 = 0.000 0.000 + 0.75x + x2 = 0 + 0.394 0.75x + x2 = 0 + 0.394 Combine like terms: 0 + 0.394 = 0.394 0.75x + x2 = 0.394 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.394 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.394 + 0.140625 Combine like terms: 0.394 + 0.140625 = 0.534625 0.140625 + 0.75x + x2 = 0.534625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.534625 Calculate the square root of the right side: 0.731180552 Break this problem into two subproblems by setting (x + 0.375) equal to 0.731180552 and -0.731180552.Subproblem 1
x + 0.375 = 0.731180552 Simplifying x + 0.375 = 0.731180552 Reorder the terms: 0.375 + x = 0.731180552 Solving 0.375 + x = 0.731180552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.731180552 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.731180552 + -0.375 x = 0.731180552 + -0.375 Combine like terms: 0.731180552 + -0.375 = 0.356180552 x = 0.356180552 Simplifying x = 0.356180552Subproblem 2
x + 0.375 = -0.731180552 Simplifying x + 0.375 = -0.731180552 Reorder the terms: 0.375 + x = -0.731180552 Solving 0.375 + x = -0.731180552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.731180552 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.731180552 + -0.375 x = -0.731180552 + -0.375 Combine like terms: -0.731180552 + -0.375 = -1.106180552 x = -1.106180552 Simplifying x = -1.106180552Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.356180552, -1.106180552}
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