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Simplifying x2 + 34x + 107 = 0 Reorder the terms: 107 + 34x + x2 = 0 Solving 107 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-107' to each side of the equation. 107 + 34x + -107 + x2 = 0 + -107 Reorder the terms: 107 + -107 + 34x + x2 = 0 + -107 Combine like terms: 107 + -107 = 0 0 + 34x + x2 = 0 + -107 34x + x2 = 0 + -107 Combine like terms: 0 + -107 = -107 34x + x2 = -107 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 = -107 + 289 Reorder the terms: 289 + 34x + x2 = -107 + 289 Combine like terms: -107 + 289 = 182 289 + 34x + x2 = 182 Factor a perfect square on the left side: (x + 17)(x + 17) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (x + 17) equal to 13.490737563 and -13.490737563.Subproblem 1
x + 17 = 13.490737563 Simplifying x + 17 = 13.490737563 Reorder the terms: 17 + x = 13.490737563 Solving 17 + x = 13.490737563 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 = 13.490737563 + -17 Combine like terms: 17 + -17 = 0 0 + x = 13.490737563 + -17 x = 13.490737563 + -17 Combine like terms: 13.490737563 + -17 = -3.509262437 x = -3.509262437 Simplifying x = -3.509262437Subproblem 2
x + 17 = -13.490737563 Simplifying x + 17 = -13.490737563 Reorder the terms: 17 + x = -13.490737563 Solving 17 + x = -13.490737563 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 = -13.490737563 + -17 Combine like terms: 17 + -17 = 0 0 + x = -13.490737563 + -17 x = -13.490737563 + -17 Combine like terms: -13.490737563 + -17 = -30.490737563 x = -30.490737563 Simplifying x = -30.490737563Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.509262437, -30.490737563}
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