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Simplifying x2 + 26x + 41 = 0 Reorder the terms: 41 + 26x + x2 = 0 Solving 41 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 26x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 26x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 26x + x2 = 0 + -41 26x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 26x + x2 = -41 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 = -41 + 169 Reorder the terms: 169 + 26x + x2 = -41 + 169 Combine like terms: -41 + 169 = 128 169 + 26x + x2 = 128 Factor a perfect square on the left side: (x + 13)(x + 13) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + 13) equal to 11.313708499 and -11.313708499.Subproblem 1
x + 13 = 11.313708499 Simplifying x + 13 = 11.313708499 Reorder the terms: 13 + x = 11.313708499 Solving 13 + x = 11.313708499 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 = 11.313708499 + -13 Combine like terms: 13 + -13 = 0 0 + x = 11.313708499 + -13 x = 11.313708499 + -13 Combine like terms: 11.313708499 + -13 = -1.686291501 x = -1.686291501 Simplifying x = -1.686291501Subproblem 2
x + 13 = -11.313708499 Simplifying x + 13 = -11.313708499 Reorder the terms: 13 + x = -11.313708499 Solving 13 + x = -11.313708499 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 = -11.313708499 + -13 Combine like terms: 13 + -13 = 0 0 + x = -11.313708499 + -13 x = -11.313708499 + -13 Combine like terms: -11.313708499 + -13 = -24.313708499 x = -24.313708499 Simplifying x = -24.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.686291501, -24.313708499}
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