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Simplifying x2 + 26x + 102 = 0 Reorder the terms: 102 + 26x + x2 = 0 Solving 102 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-102' to each side of the equation. 102 + 26x + -102 + x2 = 0 + -102 Reorder the terms: 102 + -102 + 26x + x2 = 0 + -102 Combine like terms: 102 + -102 = 0 0 + 26x + x2 = 0 + -102 26x + x2 = 0 + -102 Combine like terms: 0 + -102 = -102 26x + x2 = -102 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -102 + 169 Reorder the terms: 169 + 26x + x2 = -102 + 169 Combine like terms: -102 + 169 = 67 169 + 26x + x2 = 67 Factor a perfect square on the left side: (x + 13)(x + 13) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 13) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 13 = 8.185352772 Simplifying x + 13 = 8.185352772 Reorder the terms: 13 + x = 8.185352772 Solving 13 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 8.185352772 + -13 Combine like terms: 13 + -13 = 0 0 + x = 8.185352772 + -13 x = 8.185352772 + -13 Combine like terms: 8.185352772 + -13 = -4.814647228 x = -4.814647228 Simplifying x = -4.814647228Subproblem 2
x + 13 = -8.185352772 Simplifying x + 13 = -8.185352772 Reorder the terms: 13 + x = -8.185352772 Solving 13 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -8.185352772 + -13 Combine like terms: 13 + -13 = 0 0 + x = -8.185352772 + -13 x = -8.185352772 + -13 Combine like terms: -8.185352772 + -13 = -21.185352772 x = -21.185352772 Simplifying x = -21.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.814647228, -21.185352772}
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