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Simplifying x2 + 26x + c = 8 + c Reorder the terms: c + 26x + x2 = 8 + c Add '-1c' to each side of the equation. c + 26x + -1c + x2 = 8 + c + -1c Reorder the terms: c + -1c + 26x + x2 = 8 + c + -1c Combine like terms: c + -1c = 0 0 + 26x + x2 = 8 + c + -1c 26x + x2 = 8 + c + -1c Combine like terms: c + -1c = 0 26x + x2 = 8 + 0 26x + x2 = 8 Solving 26x + x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 26x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 26x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 26x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 26x + x2 = 0 + 8 26x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 26x + x2 = 8 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 = 8 + 169 Reorder the terms: 169 + 26x + x2 = 8 + 169 Combine like terms: 8 + 169 = 177 169 + 26x + x2 = 177 Factor a perfect square on the left side: (x + 13)(x + 13) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (x + 13) equal to 13.304134696 and -13.304134696.Subproblem 1
x + 13 = 13.304134696 Simplifying x + 13 = 13.304134696 Reorder the terms: 13 + x = 13.304134696 Solving 13 + x = 13.304134696 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 = 13.304134696 + -13 Combine like terms: 13 + -13 = 0 0 + x = 13.304134696 + -13 x = 13.304134696 + -13 Combine like terms: 13.304134696 + -13 = 0.304134696 x = 0.304134696 Simplifying x = 0.304134696Subproblem 2
x + 13 = -13.304134696 Simplifying x + 13 = -13.304134696 Reorder the terms: 13 + x = -13.304134696 Solving 13 + x = -13.304134696 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 = -13.304134696 + -13 Combine like terms: 13 + -13 = 0 0 + x = -13.304134696 + -13 x = -13.304134696 + -13 Combine like terms: -13.304134696 + -13 = -26.304134696 x = -26.304134696 Simplifying x = -26.304134696Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.304134696, -26.304134696}
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