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Simplifying 18500 = -33x2 + 1122x + 12969 Reorder the terms: 18500 = 12969 + 1122x + -33x2 Solving 18500 = 12969 + 1122x + -33x2 Solving for variable 'x'. Combine like terms: 18500 + -12969 = 5531 5531 + -1122x + 33x2 = 12969 + 1122x + -33x2 + -12969 + -1122x + 33x2 Reorder the terms: 5531 + -1122x + 33x2 = 12969 + -12969 + 1122x + -1122x + -33x2 + 33x2 Combine like terms: 12969 + -12969 = 0 5531 + -1122x + 33x2 = 0 + 1122x + -1122x + -33x2 + 33x2 5531 + -1122x + 33x2 = 1122x + -1122x + -33x2 + 33x2 Combine like terms: 1122x + -1122x = 0 5531 + -1122x + 33x2 = 0 + -33x2 + 33x2 5531 + -1122x + 33x2 = -33x2 + 33x2 Combine like terms: -33x2 + 33x2 = 0 5531 + -1122x + 33x2 = 0 Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. 167.6060606 + -34x + x2 = 0 Move the constant term to the right: Add '-167.6060606' to each side of the equation. 167.6060606 + -34x + -167.6060606 + x2 = 0 + -167.6060606 Reorder the terms: 167.6060606 + -167.6060606 + -34x + x2 = 0 + -167.6060606 Combine like terms: 167.6060606 + -167.6060606 = 0.0000000 0.0000000 + -34x + x2 = 0 + -167.6060606 -34x + x2 = 0 + -167.6060606 Combine like terms: 0 + -167.6060606 = -167.6060606 -34x + x2 = -167.6060606 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = -167.6060606 + 289 Reorder the terms: 289 + -34x + x2 = -167.6060606 + 289 Combine like terms: -167.6060606 + 289 = 121.3939394 289 + -34x + x2 = 121.3939394 Factor a perfect square on the left side: (x + -17)(x + -17) = 121.3939394 Calculate the square root of the right side: 11.017891786 Break this problem into two subproblems by setting (x + -17) equal to 11.017891786 and -11.017891786.Subproblem 1
x + -17 = 11.017891786 Simplifying x + -17 = 11.017891786 Reorder the terms: -17 + x = 11.017891786 Solving -17 + x = 11.017891786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 11.017891786 + 17 Combine like terms: -17 + 17 = 0 0 + x = 11.017891786 + 17 x = 11.017891786 + 17 Combine like terms: 11.017891786 + 17 = 28.017891786 x = 28.017891786 Simplifying x = 28.017891786Subproblem 2
x + -17 = -11.017891786 Simplifying x + -17 = -11.017891786 Reorder the terms: -17 + x = -11.017891786 Solving -17 + x = -11.017891786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -11.017891786 + 17 Combine like terms: -17 + 17 = 0 0 + x = -11.017891786 + 17 x = -11.017891786 + 17 Combine like terms: -11.017891786 + 17 = 5.982108214 x = 5.982108214 Simplifying x = 5.982108214Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.017891786, 5.982108214}
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