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Simplifying x2 + 0.0120x + -0.00332 = 0 Reorder the terms: -0.00332 + 0.0120x + x2 = 0 Solving -0.00332 + 0.0120x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.00332' to each side of the equation. -0.00332 + 0.0120x + 0.00332 + x2 = 0 + 0.00332 Reorder the terms: -0.00332 + 0.00332 + 0.0120x + x2 = 0 + 0.00332 Combine like terms: -0.00332 + 0.00332 = 0.00000 0.00000 + 0.0120x + x2 = 0 + 0.00332 0.0120x + x2 = 0 + 0.00332 Combine like terms: 0 + 0.00332 = 0.00332 0.0120x + x2 = 0.00332 The x term is 0.0120x. Take half its coefficient (0.006). Square it (0.000036) and add it to both sides. Add '0.000036' to each side of the equation. 0.0120x + 0.000036 + x2 = 0.00332 + 0.000036 Reorder the terms: 0.000036 + 0.0120x + x2 = 0.00332 + 0.000036 Combine like terms: 0.00332 + 0.000036 = 0.003356 0.000036 + 0.0120x + x2 = 0.003356 Factor a perfect square on the left side: (x + 0.006)(x + 0.006) = 0.003356 Calculate the square root of the right side: 0.057930993 Break this problem into two subproblems by setting (x + 0.006) equal to 0.057930993 and -0.057930993.Subproblem 1
x + 0.006 = 0.057930993 Simplifying x + 0.006 = 0.057930993 Reorder the terms: 0.006 + x = 0.057930993 Solving 0.006 + x = 0.057930993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.006' to each side of the equation. 0.006 + -0.006 + x = 0.057930993 + -0.006 Combine like terms: 0.006 + -0.006 = 0.000 0.000 + x = 0.057930993 + -0.006 x = 0.057930993 + -0.006 Combine like terms: 0.057930993 + -0.006 = 0.051930993 x = 0.051930993 Simplifying x = 0.051930993Subproblem 2
x + 0.006 = -0.057930993 Simplifying x + 0.006 = -0.057930993 Reorder the terms: 0.006 + x = -0.057930993 Solving 0.006 + x = -0.057930993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.006' to each side of the equation. 0.006 + -0.006 + x = -0.057930993 + -0.006 Combine like terms: 0.006 + -0.006 = 0.000 0.000 + x = -0.057930993 + -0.006 x = -0.057930993 + -0.006 Combine like terms: -0.057930993 + -0.006 = -0.063930993 x = -0.063930993 Simplifying x = -0.063930993Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.051930993, -0.063930993}
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