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Simplifying 0.00269891x2 + -0.246295547x + 0.0000256561 = 0 Reorder the terms: 0.0000256561 + -0.246295547x + 0.00269891x2 = 0 Solving 0.0000256561 + -0.246295547x + 0.00269891x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.00269891 the coefficient of the squared term: Divide each side by '0.00269891'. 0.009506096906 + -91.25741392x + x2 = 0 Move the constant term to the right: Add '-0.009506096906' to each side of the equation. 0.009506096906 + -91.25741392x + -0.009506096906 + x2 = 0 + -0.009506096906 Reorder the terms: 0.009506096906 + -0.009506096906 + -91.25741392x + x2 = 0 + -0.009506096906 Combine like terms: 0.009506096906 + -0.009506096906 = 0.000000000000 0.000000000000 + -91.25741392x + x2 = 0 + -0.009506096906 -91.25741392x + x2 = 0 + -0.009506096906 Combine like terms: 0 + -0.009506096906 = -0.009506096906 -91.25741392x + x2 = -0.009506096906 The x term is -91.25741392x. Take half its coefficient (-45.62870696). Square it (2081.978899) and add it to both sides. Add '2081.978899' to each side of the equation. -91.25741392x + 2081.978899 + x2 = -0.009506096906 + 2081.978899 Reorder the terms: 2081.978899 + -91.25741392x + x2 = -0.009506096906 + 2081.978899 Combine like terms: -0.009506096906 + 2081.978899 = 2081.969392903094 2081.978899 + -91.25741392x + x2 = 2081.969392903094 Factor a perfect square on the left side: (x + -45.62870696)(x + -45.62870696) = 2081.969392903094 Calculate the square root of the right side: 45.628602794 Break this problem into two subproblems by setting (x + -45.62870696) equal to 45.628602794 and -45.628602794.Subproblem 1
x + -45.62870696 = 45.628602794 Simplifying x + -45.62870696 = 45.628602794 Reorder the terms: -45.62870696 + x = 45.628602794 Solving -45.62870696 + x = 45.628602794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.62870696' to each side of the equation. -45.62870696 + 45.62870696 + x = 45.628602794 + 45.62870696 Combine like terms: -45.62870696 + 45.62870696 = 0.00000000 0.00000000 + x = 45.628602794 + 45.62870696 x = 45.628602794 + 45.62870696 Combine like terms: 45.628602794 + 45.62870696 = 91.257309754 x = 91.257309754 Simplifying x = 91.257309754Subproblem 2
x + -45.62870696 = -45.628602794 Simplifying x + -45.62870696 = -45.628602794 Reorder the terms: -45.62870696 + x = -45.628602794 Solving -45.62870696 + x = -45.628602794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.62870696' to each side of the equation. -45.62870696 + 45.62870696 + x = -45.628602794 + 45.62870696 Combine like terms: -45.62870696 + 45.62870696 = 0.00000000 0.00000000 + x = -45.628602794 + 45.62870696 x = -45.628602794 + 45.62870696 Combine like terms: -45.628602794 + 45.62870696 = 0.000104166 x = 0.000104166 Simplifying x = 0.000104166Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.257309754, 0.000104166}
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