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Simplifying x2 + 0.5x + -0.394 = 0 Reorder the terms: -0.394 + 0.5x + x2 = 0 Solving -0.394 + 0.5x + 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 + 0.5x + 0.394 + x2 = 0 + 0.394 Reorder the terms: -0.394 + 0.394 + 0.5x + x2 = 0 + 0.394 Combine like terms: -0.394 + 0.394 = 0.000 0.000 + 0.5x + x2 = 0 + 0.394 0.5x + x2 = 0 + 0.394 Combine like terms: 0 + 0.394 = 0.394 0.5x + x2 = 0.394 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.394 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.394 + 0.0625 Combine like terms: 0.394 + 0.0625 = 0.4565 0.0625 + 0.5x + x2 = 0.4565 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.4565 Calculate the square root of the right side: 0.675647837 Break this problem into two subproblems by setting (x + 0.25) equal to 0.675647837 and -0.675647837.Subproblem 1
x + 0.25 = 0.675647837 Simplifying x + 0.25 = 0.675647837 Reorder the terms: 0.25 + x = 0.675647837 Solving 0.25 + x = 0.675647837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.675647837 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.675647837 + -0.25 x = 0.675647837 + -0.25 Combine like terms: 0.675647837 + -0.25 = 0.425647837 x = 0.425647837 Simplifying x = 0.425647837Subproblem 2
x + 0.25 = -0.675647837 Simplifying x + 0.25 = -0.675647837 Reorder the terms: 0.25 + x = -0.675647837 Solving 0.25 + x = -0.675647837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.675647837 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.675647837 + -0.25 x = -0.675647837 + -0.25 Combine like terms: -0.675647837 + -0.25 = -0.925647837 x = -0.925647837 Simplifying x = -0.925647837Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.425647837, -0.925647837}
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