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Simplifying 0 = x2 + 0.0129x + -0.00404 Reorder the terms: 0 = -0.00404 + 0.0129x + x2 Solving 0 = -0.00404 + 0.0129x + x2 Solving for variable 'x'. Combine like terms: 0 + 0.00404 = 0.00404 0.00404 + -0.0129x + -1x2 = -0.00404 + 0.0129x + x2 + 0.00404 + -0.0129x + -1x2 Reorder the terms: 0.00404 + -0.0129x + -1x2 = -0.00404 + 0.00404 + 0.0129x + -0.0129x + x2 + -1x2 Combine like terms: -0.00404 + 0.00404 = 0.00000 0.00404 + -0.0129x + -1x2 = 0.00000 + 0.0129x + -0.0129x + x2 + -1x2 0.00404 + -0.0129x + -1x2 = 0.0129x + -0.0129x + x2 + -1x2 Combine like terms: 0.0129x + -0.0129x = 0.0000 0.00404 + -0.0129x + -1x2 = 0.0000 + x2 + -1x2 0.00404 + -0.0129x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.00404 + -0.0129x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.00404 + 0.0129x + x2 = 0 Move the constant term to the right: Add '0.00404' to each side of the equation. -0.00404 + 0.0129x + 0.00404 + x2 = 0 + 0.00404 Reorder the terms: -0.00404 + 0.00404 + 0.0129x + x2 = 0 + 0.00404 Combine like terms: -0.00404 + 0.00404 = 0.00000 0.00000 + 0.0129x + x2 = 0 + 0.00404 0.0129x + x2 = 0 + 0.00404 Combine like terms: 0 + 0.00404 = 0.00404 0.0129x + x2 = 0.00404 The x term is 0.0129x. Take half its coefficient (0.00645). Square it (0.0000416025) and add it to both sides. Add '0.0000416025' to each side of the equation. 0.0129x + 0.0000416025 + x2 = 0.00404 + 0.0000416025 Reorder the terms: 0.0000416025 + 0.0129x + x2 = 0.00404 + 0.0000416025 Combine like terms: 0.00404 + 0.0000416025 = 0.0040816025 0.0000416025 + 0.0129x + x2 = 0.0040816025 Factor a perfect square on the left side: (x + 0.00645)(x + 0.00645) = 0.0040816025 Calculate the square root of the right side: 0.063887421 Break this problem into two subproblems by setting (x + 0.00645) equal to 0.063887421 and -0.063887421.Subproblem 1
x + 0.00645 = 0.063887421 Simplifying x + 0.00645 = 0.063887421 Reorder the terms: 0.00645 + x = 0.063887421 Solving 0.00645 + x = 0.063887421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00645' to each side of the equation. 0.00645 + -0.00645 + x = 0.063887421 + -0.00645 Combine like terms: 0.00645 + -0.00645 = 0.00000 0.00000 + x = 0.063887421 + -0.00645 x = 0.063887421 + -0.00645 Combine like terms: 0.063887421 + -0.00645 = 0.057437421 x = 0.057437421 Simplifying x = 0.057437421Subproblem 2
x + 0.00645 = -0.063887421 Simplifying x + 0.00645 = -0.063887421 Reorder the terms: 0.00645 + x = -0.063887421 Solving 0.00645 + x = -0.063887421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00645' to each side of the equation. 0.00645 + -0.00645 + x = -0.063887421 + -0.00645 Combine like terms: 0.00645 + -0.00645 = 0.00000 0.00000 + x = -0.063887421 + -0.00645 x = -0.063887421 + -0.00645 Combine like terms: -0.063887421 + -0.00645 = -0.070337421 x = -0.070337421 Simplifying x = -0.070337421Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.057437421, -0.070337421}
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