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Simplifying x2 + 17x + -26 = -29x + -16 Reorder the terms: -26 + 17x + x2 = -29x + -16 Reorder the terms: -26 + 17x + x2 = -16 + -29x Solving -26 + 17x + x2 = -16 + -29x Solving for variable 'x'. Reorder the terms: -26 + 16 + 17x + 29x + x2 = -16 + -29x + 16 + 29x Combine like terms: -26 + 16 = -10 -10 + 17x + 29x + x2 = -16 + -29x + 16 + 29x Combine like terms: 17x + 29x = 46x -10 + 46x + x2 = -16 + -29x + 16 + 29x Reorder the terms: -10 + 46x + x2 = -16 + 16 + -29x + 29x Combine like terms: -16 + 16 = 0 -10 + 46x + x2 = 0 + -29x + 29x -10 + 46x + x2 = -29x + 29x Combine like terms: -29x + 29x = 0 -10 + 46x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 46x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 46x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 46x + x2 = 0 + 10 46x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 46x + x2 = 10 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = 10 + 529 Reorder the terms: 529 + 46x + x2 = 10 + 529 Combine like terms: 10 + 529 = 539 529 + 46x + x2 = 539 Factor a perfect square on the left side: (x + 23)(x + 23) = 539 Calculate the square root of the right side: 23.216373532 Break this problem into two subproblems by setting (x + 23) equal to 23.216373532 and -23.216373532.Subproblem 1
x + 23 = 23.216373532 Simplifying x + 23 = 23.216373532 Reorder the terms: 23 + x = 23.216373532 Solving 23 + x = 23.216373532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 23.216373532 + -23 Combine like terms: 23 + -23 = 0 0 + x = 23.216373532 + -23 x = 23.216373532 + -23 Combine like terms: 23.216373532 + -23 = 0.216373532 x = 0.216373532 Simplifying x = 0.216373532Subproblem 2
x + 23 = -23.216373532 Simplifying x + 23 = -23.216373532 Reorder the terms: 23 + x = -23.216373532 Solving 23 + x = -23.216373532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -23.216373532 + -23 Combine like terms: 23 + -23 = 0 0 + x = -23.216373532 + -23 x = -23.216373532 + -23 Combine like terms: -23.216373532 + -23 = -46.216373532 x = -46.216373532 Simplifying x = -46.216373532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.216373532, -46.216373532}
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