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Simplifying -1(62000) * x2 + 1274x + 5447 = 0 Multiply -1 * 62000 -62000x2 + 1274x + 5447 = 0 Reorder the terms: 5447 + 1274x + -62000x2 = 0 Solving 5447 + 1274x + -62000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -62000 the coefficient of the squared term: Divide each side by '-62000'. -0.08785483871 + -0.0205483871x + x2 = 0.000 Move the constant term to the right: Add '0.08785483871' to each side of the equation. -0.08785483871 + -0.0205483871x + 0.08785483871 + x2 = 0.000 + 0.08785483871 Reorder the terms: -0.08785483871 + 0.08785483871 + -0.0205483871x + x2 = 0.000 + 0.08785483871 Combine like terms: -0.08785483871 + 0.08785483871 = 0.00000000000 0.00000000000 + -0.0205483871x + x2 = 0.000 + 0.08785483871 -0.0205483871x + x2 = 0.000 + 0.08785483871 Combine like terms: 0.000 + 0.08785483871 = 0.08785483871 -0.0205483871x + x2 = 0.08785483871 The x term is -0.0205483871x. Take half its coefficient (-0.01027419355). Square it (0.0001055590531) and add it to both sides. Add '0.0001055590531' to each side of the equation. -0.0205483871x + 0.0001055590531 + x2 = 0.08785483871 + 0.0001055590531 Reorder the terms: 0.0001055590531 + -0.0205483871x + x2 = 0.08785483871 + 0.0001055590531 Combine like terms: 0.08785483871 + 0.0001055590531 = 0.0879603977631 0.0001055590531 + -0.0205483871x + x2 = 0.0879603977631 Factor a perfect square on the left side: (x + -0.01027419355)(x + -0.01027419355) = 0.0879603977631 Calculate the square root of the right side: 0.296581182 Break this problem into two subproblems by setting (x + -0.01027419355) equal to 0.296581182 and -0.296581182.Subproblem 1
x + -0.01027419355 = 0.296581182 Simplifying x + -0.01027419355 = 0.296581182 Reorder the terms: -0.01027419355 + x = 0.296581182 Solving -0.01027419355 + x = 0.296581182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01027419355' to each side of the equation. -0.01027419355 + 0.01027419355 + x = 0.296581182 + 0.01027419355 Combine like terms: -0.01027419355 + 0.01027419355 = 0.00000000000 0.00000000000 + x = 0.296581182 + 0.01027419355 x = 0.296581182 + 0.01027419355 Combine like terms: 0.296581182 + 0.01027419355 = 0.30685537555 x = 0.30685537555 Simplifying x = 0.30685537555Subproblem 2
x + -0.01027419355 = -0.296581182 Simplifying x + -0.01027419355 = -0.296581182 Reorder the terms: -0.01027419355 + x = -0.296581182 Solving -0.01027419355 + x = -0.296581182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01027419355' to each side of the equation. -0.01027419355 + 0.01027419355 + x = -0.296581182 + 0.01027419355 Combine like terms: -0.01027419355 + 0.01027419355 = 0.00000000000 0.00000000000 + x = -0.296581182 + 0.01027419355 x = -0.296581182 + 0.01027419355 Combine like terms: -0.296581182 + 0.01027419355 = -0.28630698845 x = -0.28630698845 Simplifying x = -0.28630698845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.30685537555, -0.28630698845}
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