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Simplifying x2 + 0.0064x + -0.13 = 0 Reorder the terms: -0.13 + 0.0064x + x2 = 0 Solving -0.13 + 0.0064x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.13' to each side of the equation. -0.13 + 0.0064x + 0.13 + x2 = 0 + 0.13 Reorder the terms: -0.13 + 0.13 + 0.0064x + x2 = 0 + 0.13 Combine like terms: -0.13 + 0.13 = 0.00 0.00 + 0.0064x + x2 = 0 + 0.13 0.0064x + x2 = 0 + 0.13 Combine like terms: 0 + 0.13 = 0.13 0.0064x + x2 = 0.13 The x term is 0.0064x. Take half its coefficient (0.0032). Square it (0.00001024) and add it to both sides. Add '0.00001024' to each side of the equation. 0.0064x + 0.00001024 + x2 = 0.13 + 0.00001024 Reorder the terms: 0.00001024 + 0.0064x + x2 = 0.13 + 0.00001024 Combine like terms: 0.13 + 0.00001024 = 0.13001024 0.00001024 + 0.0064x + x2 = 0.13001024 Factor a perfect square on the left side: (x + 0.0032)(x + 0.0032) = 0.13001024 Calculate the square root of the right side: 0.360569328 Break this problem into two subproblems by setting (x + 0.0032) equal to 0.360569328 and -0.360569328.Subproblem 1
x + 0.0032 = 0.360569328 Simplifying x + 0.0032 = 0.360569328 Reorder the terms: 0.0032 + x = 0.360569328 Solving 0.0032 + x = 0.360569328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0032' to each side of the equation. 0.0032 + -0.0032 + x = 0.360569328 + -0.0032 Combine like terms: 0.0032 + -0.0032 = 0.0000 0.0000 + x = 0.360569328 + -0.0032 x = 0.360569328 + -0.0032 Combine like terms: 0.360569328 + -0.0032 = 0.357369328 x = 0.357369328 Simplifying x = 0.357369328Subproblem 2
x + 0.0032 = -0.360569328 Simplifying x + 0.0032 = -0.360569328 Reorder the terms: 0.0032 + x = -0.360569328 Solving 0.0032 + x = -0.360569328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0032' to each side of the equation. 0.0032 + -0.0032 + x = -0.360569328 + -0.0032 Combine like terms: 0.0032 + -0.0032 = 0.0000 0.0000 + x = -0.360569328 + -0.0032 x = -0.360569328 + -0.0032 Combine like terms: -0.360569328 + -0.0032 = -0.363769328 x = -0.363769328 Simplifying x = -0.363769328Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.357369328, -0.363769328}
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