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Simplifying 0.0627 = x2 + 0.190x Reorder the terms: 0.0627 = 0.190x + x2 Solving 0.0627 = 0.190x + x2 Solving for variable 'x'. Reorder the terms: 0.0627 + -0.190x + -1x2 = 0.190x + -0.190x + x2 + -1x2 Combine like terms: 0.190x + -0.190x = 0.000 0.0627 + -0.190x + -1x2 = 0.000 + x2 + -1x2 0.0627 + -0.190x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.0627 + -0.190x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.0627 + 0.19x + x2 = 0 Move the constant term to the right: Add '0.0627' to each side of the equation. -0.0627 + 0.19x + 0.0627 + x2 = 0 + 0.0627 Reorder the terms: -0.0627 + 0.0627 + 0.19x + x2 = 0 + 0.0627 Combine like terms: -0.0627 + 0.0627 = 0.0000 0.0000 + 0.19x + x2 = 0 + 0.0627 0.19x + x2 = 0 + 0.0627 Combine like terms: 0 + 0.0627 = 0.0627 0.19x + x2 = 0.0627 The x term is 0.19x. Take half its coefficient (0.095). Square it (0.009025) and add it to both sides. Add '0.009025' to each side of the equation. 0.19x + 0.009025 + x2 = 0.0627 + 0.009025 Reorder the terms: 0.009025 + 0.19x + x2 = 0.0627 + 0.009025 Combine like terms: 0.0627 + 0.009025 = 0.071725 0.009025 + 0.19x + x2 = 0.071725 Factor a perfect square on the left side: (x + 0.095)(x + 0.095) = 0.071725 Calculate the square root of the right side: 0.267815235 Break this problem into two subproblems by setting (x + 0.095) equal to 0.267815235 and -0.267815235.Subproblem 1
x + 0.095 = 0.267815235 Simplifying x + 0.095 = 0.267815235 Reorder the terms: 0.095 + x = 0.267815235 Solving 0.095 + x = 0.267815235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.095' to each side of the equation. 0.095 + -0.095 + x = 0.267815235 + -0.095 Combine like terms: 0.095 + -0.095 = 0.000 0.000 + x = 0.267815235 + -0.095 x = 0.267815235 + -0.095 Combine like terms: 0.267815235 + -0.095 = 0.172815235 x = 0.172815235 Simplifying x = 0.172815235Subproblem 2
x + 0.095 = -0.267815235 Simplifying x + 0.095 = -0.267815235 Reorder the terms: 0.095 + x = -0.267815235 Solving 0.095 + x = -0.267815235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.095' to each side of the equation. 0.095 + -0.095 + x = -0.267815235 + -0.095 Combine like terms: 0.095 + -0.095 = 0.000 0.000 + x = -0.267815235 + -0.095 x = -0.267815235 + -0.095 Combine like terms: -0.267815235 + -0.095 = -0.362815235 x = -0.362815235 Simplifying x = -0.362815235Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.172815235, -0.362815235}
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