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Simplifying X2 + 0.166X + -0.166 = 0 Reorder the terms: -0.166 + 0.166X + X2 = 0 Solving -0.166 + 0.166X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '0.166' to each side of the equation. -0.166 + 0.166X + 0.166 + X2 = 0 + 0.166 Reorder the terms: -0.166 + 0.166 + 0.166X + X2 = 0 + 0.166 Combine like terms: -0.166 + 0.166 = 0.000 0.000 + 0.166X + X2 = 0 + 0.166 0.166X + X2 = 0 + 0.166 Combine like terms: 0 + 0.166 = 0.166 0.166X + X2 = 0.166 The X term is 0.166X. Take half its coefficient (0.083). Square it (0.006889) and add it to both sides. Add '0.006889' to each side of the equation. 0.166X + 0.006889 + X2 = 0.166 + 0.006889 Reorder the terms: 0.006889 + 0.166X + X2 = 0.166 + 0.006889 Combine like terms: 0.166 + 0.006889 = 0.172889 0.006889 + 0.166X + X2 = 0.172889 Factor a perfect square on the left side: (X + 0.083)(X + 0.083) = 0.172889 Calculate the square root of the right side: 0.41579923 Break this problem into two subproblems by setting (X + 0.083) equal to 0.41579923 and -0.41579923.Subproblem 1
X + 0.083 = 0.41579923 Simplifying X + 0.083 = 0.41579923 Reorder the terms: 0.083 + X = 0.41579923 Solving 0.083 + X = 0.41579923 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.083' to each side of the equation. 0.083 + -0.083 + X = 0.41579923 + -0.083 Combine like terms: 0.083 + -0.083 = 0.000 0.000 + X = 0.41579923 + -0.083 X = 0.41579923 + -0.083 Combine like terms: 0.41579923 + -0.083 = 0.33279923 X = 0.33279923 Simplifying X = 0.33279923Subproblem 2
X + 0.083 = -0.41579923 Simplifying X + 0.083 = -0.41579923 Reorder the terms: 0.083 + X = -0.41579923 Solving 0.083 + X = -0.41579923 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.083' to each side of the equation. 0.083 + -0.083 + X = -0.41579923 + -0.083 Combine like terms: 0.083 + -0.083 = 0.000 0.000 + X = -0.41579923 + -0.083 X = -0.41579923 + -0.083 Combine like terms: -0.41579923 + -0.083 = -0.49879923 X = -0.49879923 Simplifying X = -0.49879923Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.33279923, -0.49879923}
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