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Simplifying 1728 = x2 + 34x Reorder the terms: 1728 = 34x + x2 Solving 1728 = 34x + x2 Solving for variable 'x'. Reorder the terms: 1728 + -34x + -1x2 = 34x + -34x + x2 + -1x2 Combine like terms: 34x + -34x = 0 1728 + -34x + -1x2 = 0 + x2 + -1x2 1728 + -34x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1728 + -34x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1728 + 34x + x2 = 0 Move the constant term to the right: Add '1728' to each side of the equation. -1728 + 34x + 1728 + x2 = 0 + 1728 Reorder the terms: -1728 + 1728 + 34x + x2 = 0 + 1728 Combine like terms: -1728 + 1728 = 0 0 + 34x + x2 = 0 + 1728 34x + x2 = 0 + 1728 Combine like terms: 0 + 1728 = 1728 34x + x2 = 1728 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 = 1728 + 289 Reorder the terms: 289 + 34x + x2 = 1728 + 289 Combine like terms: 1728 + 289 = 2017 289 + 34x + x2 = 2017 Factor a perfect square on the left side: (x + 17)(x + 17) = 2017 Calculate the square root of the right side: 44.911023146 Break this problem into two subproblems by setting (x + 17) equal to 44.911023146 and -44.911023146.Subproblem 1
x + 17 = 44.911023146 Simplifying x + 17 = 44.911023146 Reorder the terms: 17 + x = 44.911023146 Solving 17 + x = 44.911023146 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 = 44.911023146 + -17 Combine like terms: 17 + -17 = 0 0 + x = 44.911023146 + -17 x = 44.911023146 + -17 Combine like terms: 44.911023146 + -17 = 27.911023146 x = 27.911023146 Simplifying x = 27.911023146Subproblem 2
x + 17 = -44.911023146 Simplifying x + 17 = -44.911023146 Reorder the terms: 17 + x = -44.911023146 Solving 17 + x = -44.911023146 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 = -44.911023146 + -17 Combine like terms: 17 + -17 = 0 0 + x = -44.911023146 + -17 x = -44.911023146 + -17 Combine like terms: -44.911023146 + -17 = -61.911023146 x = -61.911023146 Simplifying x = -61.911023146Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.911023146, -61.911023146}
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