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Simplifying x * x + (0.00416) * x + -0.00416 = 0 Multiply x * x x2 + (0.00416) * x + -0.00416 = 0 Reorder the terms: -0.00416 + 0.00416x + x2 = 0 Solving -0.00416 + 0.00416x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.00416' to each side of the equation. -0.00416 + 0.00416x + 0.00416 + x2 = 0 + 0.00416 Reorder the terms: -0.00416 + 0.00416 + 0.00416x + x2 = 0 + 0.00416 Combine like terms: -0.00416 + 0.00416 = 0.00000 0.00000 + 0.00416x + x2 = 0 + 0.00416 0.00416x + x2 = 0 + 0.00416 Combine like terms: 0 + 0.00416 = 0.00416 0.00416x + x2 = 0.00416 The x term is 0.00416x. Take half its coefficient (0.00208). Square it (0.0000043264) and add it to both sides. Add '0.0000043264' to each side of the equation. 0.00416x + 0.0000043264 + x2 = 0.00416 + 0.0000043264 Reorder the terms: 0.0000043264 + 0.00416x + x2 = 0.00416 + 0.0000043264 Combine like terms: 0.00416 + 0.0000043264 = 0.0041643264 0.0000043264 + 0.00416x + x2 = 0.0041643264 Factor a perfect square on the left side: (x + 0.00208)(x + 0.00208) = 0.0041643264 Calculate the square root of the right side: 0.064531592 Break this problem into two subproblems by setting (x + 0.00208) equal to 0.064531592 and -0.064531592.Subproblem 1
x + 0.00208 = 0.064531592 Simplifying x + 0.00208 = 0.064531592 Reorder the terms: 0.00208 + x = 0.064531592 Solving 0.00208 + x = 0.064531592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00208' to each side of the equation. 0.00208 + -0.00208 + x = 0.064531592 + -0.00208 Combine like terms: 0.00208 + -0.00208 = 0.00000 0.00000 + x = 0.064531592 + -0.00208 x = 0.064531592 + -0.00208 Combine like terms: 0.064531592 + -0.00208 = 0.062451592 x = 0.062451592 Simplifying x = 0.062451592Subproblem 2
x + 0.00208 = -0.064531592 Simplifying x + 0.00208 = -0.064531592 Reorder the terms: 0.00208 + x = -0.064531592 Solving 0.00208 + x = -0.064531592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00208' to each side of the equation. 0.00208 + -0.00208 + x = -0.064531592 + -0.00208 Combine like terms: 0.00208 + -0.00208 = 0.00000 0.00000 + x = -0.064531592 + -0.00208 x = -0.064531592 + -0.00208 Combine like terms: -0.064531592 + -0.00208 = -0.066611592 x = -0.066611592 Simplifying x = -0.066611592Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.062451592, -0.066611592}
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