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Simplifying 0.051x2 + 419x + -33271 = 0 Reorder the terms: -33271 + 419x + 0.051x2 = 0 Solving -33271 + 419x + 0.051x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.051 the coefficient of the squared term: Divide each side by '0.051'. -652372.549 + 8215.686275x + x2 = 0 Move the constant term to the right: Add '652372.549' to each side of the equation. -652372.549 + 8215.686275x + 652372.549 + x2 = 0 + 652372.549 Reorder the terms: -652372.549 + 652372.549 + 8215.686275x + x2 = 0 + 652372.549 Combine like terms: -652372.549 + 652372.549 = 0.000 0.000 + 8215.686275x + x2 = 0 + 652372.549 8215.686275x + x2 = 0 + 652372.549 Combine like terms: 0 + 652372.549 = 652372.549 8215.686275x + x2 = 652372.549 The x term is 8215.686275x. Take half its coefficient (4107.843138). Square it (16874375.25) and add it to both sides. Add '16874375.25' to each side of the equation. 8215.686275x + 16874375.25 + x2 = 652372.549 + 16874375.25 Reorder the terms: 16874375.25 + 8215.686275x + x2 = 652372.549 + 16874375.25 Combine like terms: 652372.549 + 16874375.25 = 17526747.799 16874375.25 + 8215.686275x + x2 = 17526747.799 Factor a perfect square on the left side: (x + 4107.843138)(x + 4107.843138) = 17526747.799 Calculate the square root of the right side: 4186.495885463 Break this problem into two subproblems by setting (x + 4107.843138) equal to 4186.495885463 and -4186.495885463.Subproblem 1
x + 4107.843138 = 4186.495885463 Simplifying x + 4107.843138 = 4186.495885463 Reorder the terms: 4107.843138 + x = 4186.495885463 Solving 4107.843138 + x = 4186.495885463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4107.843138' to each side of the equation. 4107.843138 + -4107.843138 + x = 4186.495885463 + -4107.843138 Combine like terms: 4107.843138 + -4107.843138 = 0.000000 0.000000 + x = 4186.495885463 + -4107.843138 x = 4186.495885463 + -4107.843138 Combine like terms: 4186.495885463 + -4107.843138 = 78.652747463 x = 78.652747463 Simplifying x = 78.652747463Subproblem 2
x + 4107.843138 = -4186.495885463 Simplifying x + 4107.843138 = -4186.495885463 Reorder the terms: 4107.843138 + x = -4186.495885463 Solving 4107.843138 + x = -4186.495885463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4107.843138' to each side of the equation. 4107.843138 + -4107.843138 + x = -4186.495885463 + -4107.843138 Combine like terms: 4107.843138 + -4107.843138 = 0.000000 0.000000 + x = -4186.495885463 + -4107.843138 x = -4186.495885463 + -4107.843138 Combine like terms: -4186.495885463 + -4107.843138 = -8294.339023463 x = -8294.339023463 Simplifying x = -8294.339023463Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.652747463, -8294.339023463}
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