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Simplifying x2 + 0.113x + -0.013 = 0 Reorder the terms: -0.013 + 0.113x + x2 = 0 Solving -0.013 + 0.113x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.013' to each side of the equation. -0.013 + 0.113x + 0.013 + x2 = 0 + 0.013 Reorder the terms: -0.013 + 0.013 + 0.113x + x2 = 0 + 0.013 Combine like terms: -0.013 + 0.013 = 0.000 0.000 + 0.113x + x2 = 0 + 0.013 0.113x + x2 = 0 + 0.013 Combine like terms: 0 + 0.013 = 0.013 0.113x + x2 = 0.013 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 = 0.013 + 0.00319225 Reorder the terms: 0.00319225 + 0.113x + x2 = 0.013 + 0.00319225 Combine like terms: 0.013 + 0.00319225 = 0.01619225 0.00319225 + 0.113x + x2 = 0.01619225 Factor a perfect square on the left side: (x + 0.0565)(x + 0.0565) = 0.01619225 Calculate the square root of the right side: 0.127248772 Break this problem into two subproblems by setting (x + 0.0565) equal to 0.127248772 and -0.127248772.Subproblem 1
x + 0.0565 = 0.127248772 Simplifying x + 0.0565 = 0.127248772 Reorder the terms: 0.0565 + x = 0.127248772 Solving 0.0565 + x = 0.127248772 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 = 0.127248772 + -0.0565 Combine like terms: 0.0565 + -0.0565 = 0.0000 0.0000 + x = 0.127248772 + -0.0565 x = 0.127248772 + -0.0565 Combine like terms: 0.127248772 + -0.0565 = 0.070748772 x = 0.070748772 Simplifying x = 0.070748772Subproblem 2
x + 0.0565 = -0.127248772 Simplifying x + 0.0565 = -0.127248772 Reorder the terms: 0.0565 + x = -0.127248772 Solving 0.0565 + x = -0.127248772 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 = -0.127248772 + -0.0565 Combine like terms: 0.0565 + -0.0565 = 0.0000 0.0000 + x = -0.127248772 + -0.0565 x = -0.127248772 + -0.0565 Combine like terms: -0.127248772 + -0.0565 = -0.183748772 x = -0.183748772 Simplifying x = -0.183748772Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.070748772, -0.183748772}
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