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Simplifying 2266x2 + 5257x = 81645 Reorder the terms: 5257x + 2266x2 = 81645 Solving 5257x + 2266x2 = 81645 Solving for variable 'x'. Reorder the terms: -81645 + 5257x + 2266x2 = 81645 + -81645 Combine like terms: 81645 + -81645 = 0 -81645 + 5257x + 2266x2 = 0 Begin completing the square. Divide all terms by 2266 the coefficient of the squared term: Divide each side by '2266'. -36.03045013 + 2.319947043x + x2 = 0 Move the constant term to the right: Add '36.03045013' to each side of the equation. -36.03045013 + 2.319947043x + 36.03045013 + x2 = 0 + 36.03045013 Reorder the terms: -36.03045013 + 36.03045013 + 2.319947043x + x2 = 0 + 36.03045013 Combine like terms: -36.03045013 + 36.03045013 = 0.00000000 0.00000000 + 2.319947043x + x2 = 0 + 36.03045013 2.319947043x + x2 = 0 + 36.03045013 Combine like terms: 0 + 36.03045013 = 36.03045013 2.319947043x + x2 = 36.03045013 The x term is 2.319947043x. Take half its coefficient (1.159973522). Square it (1.345538572) and add it to both sides. Add '1.345538572' to each side of the equation. 2.319947043x + 1.345538572 + x2 = 36.03045013 + 1.345538572 Reorder the terms: 1.345538572 + 2.319947043x + x2 = 36.03045013 + 1.345538572 Combine like terms: 36.03045013 + 1.345538572 = 37.375988702 1.345538572 + 2.319947043x + x2 = 37.375988702 Factor a perfect square on the left side: (x + 1.159973522)(x + 1.159973522) = 37.375988702 Calculate the square root of the right side: 6.113590492 Break this problem into two subproblems by setting (x + 1.159973522) equal to 6.113590492 and -6.113590492.Subproblem 1
x + 1.159973522 = 6.113590492 Simplifying x + 1.159973522 = 6.113590492 Reorder the terms: 1.159973522 + x = 6.113590492 Solving 1.159973522 + x = 6.113590492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.159973522' to each side of the equation. 1.159973522 + -1.159973522 + x = 6.113590492 + -1.159973522 Combine like terms: 1.159973522 + -1.159973522 = 0.000000000 0.000000000 + x = 6.113590492 + -1.159973522 x = 6.113590492 + -1.159973522 Combine like terms: 6.113590492 + -1.159973522 = 4.95361697 x = 4.95361697 Simplifying x = 4.95361697Subproblem 2
x + 1.159973522 = -6.113590492 Simplifying x + 1.159973522 = -6.113590492 Reorder the terms: 1.159973522 + x = -6.113590492 Solving 1.159973522 + x = -6.113590492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.159973522' to each side of the equation. 1.159973522 + -1.159973522 + x = -6.113590492 + -1.159973522 Combine like terms: 1.159973522 + -1.159973522 = 0.000000000 0.000000000 + x = -6.113590492 + -1.159973522 x = -6.113590492 + -1.159973522 Combine like terms: -6.113590492 + -1.159973522 = -7.273564014 x = -7.273564014 Simplifying x = -7.273564014Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.95361697, -7.273564014}
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