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Simplifying x2 + 26x + 91 = 0 Reorder the terms: 91 + 26x + x2 = 0 Solving 91 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-91' to each side of the equation. 91 + 26x + -91 + x2 = 0 + -91 Reorder the terms: 91 + -91 + 26x + x2 = 0 + -91 Combine like terms: 91 + -91 = 0 0 + 26x + x2 = 0 + -91 26x + x2 = 0 + -91 Combine like terms: 0 + -91 = -91 26x + x2 = -91 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 = -91 + 169 Reorder the terms: 169 + 26x + x2 = -91 + 169 Combine like terms: -91 + 169 = 78 169 + 26x + x2 = 78 Factor a perfect square on the left side: (x + 13)(x + 13) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + 13) equal to 8.831760866 and -8.831760866.Subproblem 1
x + 13 = 8.831760866 Simplifying x + 13 = 8.831760866 Reorder the terms: 13 + x = 8.831760866 Solving 13 + x = 8.831760866 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 = 8.831760866 + -13 Combine like terms: 13 + -13 = 0 0 + x = 8.831760866 + -13 x = 8.831760866 + -13 Combine like terms: 8.831760866 + -13 = -4.168239134 x = -4.168239134 Simplifying x = -4.168239134Subproblem 2
x + 13 = -8.831760866 Simplifying x + 13 = -8.831760866 Reorder the terms: 13 + x = -8.831760866 Solving 13 + x = -8.831760866 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 = -8.831760866 + -13 Combine like terms: 13 + -13 = 0 0 + x = -8.831760866 + -13 x = -8.831760866 + -13 Combine like terms: -8.831760866 + -13 = -21.831760866 x = -21.831760866 Simplifying x = -21.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.168239134, -21.831760866}
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