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Simplifying x2 + 0.113x + -0.0013 = 0 Reorder the terms: -0.0013 + 0.113x + x2 = 0 Solving -0.0013 + 0.113x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0013' to each side of the equation. -0.0013 + 0.113x + 0.0013 + x2 = 0 + 0.0013 Reorder the terms: -0.0013 + 0.0013 + 0.113x + x2 = 0 + 0.0013 Combine like terms: -0.0013 + 0.0013 = 0.0000 0.0000 + 0.113x + x2 = 0 + 0.0013 0.113x + x2 = 0 + 0.0013 Combine like terms: 0 + 0.0013 = 0.0013 0.113x + x2 = 0.0013 The x term is 0.113x. Take half its coefficient (0.0565). Square it (0.00319225) and add it to both sides. Add '0.00319225' to each side of the equation. 0.113x + 0.00319225 + x2 = 0.0013 + 0.00319225 Reorder the terms: 0.00319225 + 0.113x + x2 = 0.0013 + 0.00319225 Combine like terms: 0.0013 + 0.00319225 = 0.00449225 0.00319225 + 0.113x + x2 = 0.00449225 Factor a perfect square on the left side: (x + 0.0565)(x + 0.0565) = 0.00449225 Calculate the square root of the right side: 0.067024249 Break this problem into two subproblems by setting (x + 0.0565) equal to 0.067024249 and -0.067024249.Subproblem 1
x + 0.0565 = 0.067024249 Simplifying x + 0.0565 = 0.067024249 Reorder the terms: 0.0565 + x = 0.067024249 Solving 0.0565 + x = 0.067024249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0565' to each side of the equation. 0.0565 + -0.0565 + x = 0.067024249 + -0.0565 Combine like terms: 0.0565 + -0.0565 = 0.0000 0.0000 + x = 0.067024249 + -0.0565 x = 0.067024249 + -0.0565 Combine like terms: 0.067024249 + -0.0565 = 0.010524249 x = 0.010524249 Simplifying x = 0.010524249Subproblem 2
x + 0.0565 = -0.067024249 Simplifying x + 0.0565 = -0.067024249 Reorder the terms: 0.0565 + x = -0.067024249 Solving 0.0565 + x = -0.067024249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0565' to each side of the equation. 0.0565 + -0.0565 + x = -0.067024249 + -0.0565 Combine like terms: 0.0565 + -0.0565 = 0.0000 0.0000 + x = -0.067024249 + -0.0565 x = -0.067024249 + -0.0565 Combine like terms: -0.067024249 + -0.0565 = -0.123524249 x = -0.123524249 Simplifying x = -0.123524249Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.010524249, -0.123524249}
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