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Simplifying x2 + 16.66x + -0.66 = 0 Reorder the terms: -0.66 + 16.66x + x2 = 0 Solving -0.66 + 16.66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.66' to each side of the equation. -0.66 + 16.66x + 0.66 + x2 = 0 + 0.66 Reorder the terms: -0.66 + 0.66 + 16.66x + x2 = 0 + 0.66 Combine like terms: -0.66 + 0.66 = 0.00 0.00 + 16.66x + x2 = 0 + 0.66 16.66x + x2 = 0 + 0.66 Combine like terms: 0 + 0.66 = 0.66 16.66x + x2 = 0.66 The x term is 16.66x. Take half its coefficient (8.33). Square it (69.3889) and add it to both sides. Add '69.3889' to each side of the equation. 16.66x + 69.3889 + x2 = 0.66 + 69.3889 Reorder the terms: 69.3889 + 16.66x + x2 = 0.66 + 69.3889 Combine like terms: 0.66 + 69.3889 = 70.0489 69.3889 + 16.66x + x2 = 70.0489 Factor a perfect square on the left side: (x + 8.33)(x + 8.33) = 70.0489 Calculate the square root of the right side: 8.369522089 Break this problem into two subproblems by setting (x + 8.33) equal to 8.369522089 and -8.369522089.Subproblem 1
x + 8.33 = 8.369522089 Simplifying x + 8.33 = 8.369522089 Reorder the terms: 8.33 + x = 8.369522089 Solving 8.33 + x = 8.369522089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.33' to each side of the equation. 8.33 + -8.33 + x = 8.369522089 + -8.33 Combine like terms: 8.33 + -8.33 = 0.00 0.00 + x = 8.369522089 + -8.33 x = 8.369522089 + -8.33 Combine like terms: 8.369522089 + -8.33 = 0.039522089 x = 0.039522089 Simplifying x = 0.039522089Subproblem 2
x + 8.33 = -8.369522089 Simplifying x + 8.33 = -8.369522089 Reorder the terms: 8.33 + x = -8.369522089 Solving 8.33 + x = -8.369522089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.33' to each side of the equation. 8.33 + -8.33 + x = -8.369522089 + -8.33 Combine like terms: 8.33 + -8.33 = 0.00 0.00 + x = -8.369522089 + -8.33 x = -8.369522089 + -8.33 Combine like terms: -8.369522089 + -8.33 = -16.699522089 x = -16.699522089 Simplifying x = -16.699522089Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.039522089, -16.699522089}
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