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Simplifying x2 + 0.0075x + -0.00485 = 0 Reorder the terms: -0.00485 + 0.0075x + x2 = 0 Solving -0.00485 + 0.0075x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.00485' to each side of the equation. -0.00485 + 0.0075x + 0.00485 + x2 = 0 + 0.00485 Reorder the terms: -0.00485 + 0.00485 + 0.0075x + x2 = 0 + 0.00485 Combine like terms: -0.00485 + 0.00485 = 0.00000 0.00000 + 0.0075x + x2 = 0 + 0.00485 0.0075x + x2 = 0 + 0.00485 Combine like terms: 0 + 0.00485 = 0.00485 0.0075x + x2 = 0.00485 The x term is 0.0075x. Take half its coefficient (0.00375). Square it (0.0000140625) and add it to both sides. Add '0.0000140625' to each side of the equation. 0.0075x + 0.0000140625 + x2 = 0.00485 + 0.0000140625 Reorder the terms: 0.0000140625 + 0.0075x + x2 = 0.00485 + 0.0000140625 Combine like terms: 0.00485 + 0.0000140625 = 0.0048640625 0.0000140625 + 0.0075x + x2 = 0.0048640625 Factor a perfect square on the left side: (x + 0.00375)(x + 0.00375) = 0.0048640625 Calculate the square root of the right side: 0.069742831 Break this problem into two subproblems by setting (x + 0.00375) equal to 0.069742831 and -0.069742831.Subproblem 1
x + 0.00375 = 0.069742831 Simplifying x + 0.00375 = 0.069742831 Reorder the terms: 0.00375 + x = 0.069742831 Solving 0.00375 + x = 0.069742831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00375' to each side of the equation. 0.00375 + -0.00375 + x = 0.069742831 + -0.00375 Combine like terms: 0.00375 + -0.00375 = 0.00000 0.00000 + x = 0.069742831 + -0.00375 x = 0.069742831 + -0.00375 Combine like terms: 0.069742831 + -0.00375 = 0.065992831 x = 0.065992831 Simplifying x = 0.065992831Subproblem 2
x + 0.00375 = -0.069742831 Simplifying x + 0.00375 = -0.069742831 Reorder the terms: 0.00375 + x = -0.069742831 Solving 0.00375 + x = -0.069742831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00375' to each side of the equation. 0.00375 + -0.00375 + x = -0.069742831 + -0.00375 Combine like terms: 0.00375 + -0.00375 = 0.00000 0.00000 + x = -0.069742831 + -0.00375 x = -0.069742831 + -0.00375 Combine like terms: -0.069742831 + -0.00375 = -0.073492831 x = -0.073492831 Simplifying x = -0.073492831Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.065992831, -0.073492831}
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