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Simplifying 5645 + 13418x + -131 = 181x2 + -12 + 131 Reorder the terms: 5645 + -131 + 13418x = 181x2 + -12 + 131 Combine like terms: 5645 + -131 = 5514 5514 + 13418x = 181x2 + -12 + 131 Reorder the terms: 5514 + 13418x = -12 + 131 + 181x2 Combine like terms: -12 + 131 = 119 5514 + 13418x = 119 + 181x2 Solving 5514 + 13418x = 119 + 181x2 Solving for variable 'x'. Reorder the terms: 5514 + -119 + 13418x + -181x2 = 119 + 181x2 + -119 + -181x2 Combine like terms: 5514 + -119 = 5395 5395 + 13418x + -181x2 = 119 + 181x2 + -119 + -181x2 Reorder the terms: 5395 + 13418x + -181x2 = 119 + -119 + 181x2 + -181x2 Combine like terms: 119 + -119 = 0 5395 + 13418x + -181x2 = 0 + 181x2 + -181x2 5395 + 13418x + -181x2 = 181x2 + -181x2 Combine like terms: 181x2 + -181x2 = 0 5395 + 13418x + -181x2 = 0 Begin completing the square. Divide all terms by -181 the coefficient of the squared term: Divide each side by '-181'. -29.80662983 + -74.13259669x + x2 = 0 Move the constant term to the right: Add '29.80662983' to each side of the equation. -29.80662983 + -74.13259669x + 29.80662983 + x2 = 0 + 29.80662983 Reorder the terms: -29.80662983 + 29.80662983 + -74.13259669x + x2 = 0 + 29.80662983 Combine like terms: -29.80662983 + 29.80662983 = 0.00000000 0.00000000 + -74.13259669x + x2 = 0 + 29.80662983 -74.13259669x + x2 = 0 + 29.80662983 Combine like terms: 0 + 29.80662983 = 29.80662983 -74.13259669x + x2 = 29.80662983 The x term is -74.13259669x. Take half its coefficient (-37.06629835). Square it (1373.910473) and add it to both sides. Add '1373.910473' to each side of the equation. -74.13259669x + 1373.910473 + x2 = 29.80662983 + 1373.910473 Reorder the terms: 1373.910473 + -74.13259669x + x2 = 29.80662983 + 1373.910473 Combine like terms: 29.80662983 + 1373.910473 = 1403.71710283 1373.910473 + -74.13259669x + x2 = 1403.71710283 Factor a perfect square on the left side: (x + -37.06629835)(x + -37.06629835) = 1403.71710283 Calculate the square root of the right side: 37.466212817 Break this problem into two subproblems by setting (x + -37.06629835) equal to 37.466212817 and -37.466212817.Subproblem 1
x + -37.06629835 = 37.466212817 Simplifying x + -37.06629835 = 37.466212817 Reorder the terms: -37.06629835 + x = 37.466212817 Solving -37.06629835 + x = 37.466212817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.06629835' to each side of the equation. -37.06629835 + 37.06629835 + x = 37.466212817 + 37.06629835 Combine like terms: -37.06629835 + 37.06629835 = 0.00000000 0.00000000 + x = 37.466212817 + 37.06629835 x = 37.466212817 + 37.06629835 Combine like terms: 37.466212817 + 37.06629835 = 74.532511167 x = 74.532511167 Simplifying x = 74.532511167Subproblem 2
x + -37.06629835 = -37.466212817 Simplifying x + -37.06629835 = -37.466212817 Reorder the terms: -37.06629835 + x = -37.466212817 Solving -37.06629835 + x = -37.466212817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.06629835' to each side of the equation. -37.06629835 + 37.06629835 + x = -37.466212817 + 37.06629835 Combine like terms: -37.06629835 + 37.06629835 = 0.00000000 0.00000000 + x = -37.466212817 + 37.06629835 x = -37.466212817 + 37.06629835 Combine like terms: -37.466212817 + 37.06629835 = -0.399914467 x = -0.399914467 Simplifying x = -0.399914467Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.532511167, -0.399914467}
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