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Simplifying x + (x + 25) * x + -26 = 25 + 26 Reorder the terms: x + (25 + x) * x + -26 = 25 + 26 Reorder the terms for easier multiplication: x + x(25 + x) + -26 = 25 + 26 x + (25 * x + x * x) + -26 = 25 + 26 x + (25x + x2) + -26 = 25 + 26 Reorder the terms: -26 + x + 25x + x2 = 25 + 26 Combine like terms: x + 25x = 26x -26 + 26x + x2 = 25 + 26 Combine like terms: 25 + 26 = 51 -26 + 26x + x2 = 51 Solving -26 + 26x + x2 = 51 Solving for variable 'x'. Reorder the terms: -26 + -51 + 26x + x2 = 51 + -51 Combine like terms: -26 + -51 = -77 -77 + 26x + x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -77 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 26x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 26x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 26x + x2 = 0 + 77 26x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 26x + x2 = 77 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 = 77 + 169 Reorder the terms: 169 + 26x + x2 = 77 + 169 Combine like terms: 77 + 169 = 246 169 + 26x + x2 = 246 Factor a perfect square on the left side: (x + 13)(x + 13) = 246 Calculate the square root of the right side: 15.684387141 Break this problem into two subproblems by setting (x + 13) equal to 15.684387141 and -15.684387141.Subproblem 1
x + 13 = 15.684387141 Simplifying x + 13 = 15.684387141 Reorder the terms: 13 + x = 15.684387141 Solving 13 + x = 15.684387141 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 = 15.684387141 + -13 Combine like terms: 13 + -13 = 0 0 + x = 15.684387141 + -13 x = 15.684387141 + -13 Combine like terms: 15.684387141 + -13 = 2.684387141 x = 2.684387141 Simplifying x = 2.684387141Subproblem 2
x + 13 = -15.684387141 Simplifying x + 13 = -15.684387141 Reorder the terms: 13 + x = -15.684387141 Solving 13 + x = -15.684387141 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 = -15.684387141 + -13 Combine like terms: 13 + -13 = 0 0 + x = -15.684387141 + -13 x = -15.684387141 + -13 Combine like terms: -15.684387141 + -13 = -28.684387141 x = -28.684387141 Simplifying x = -28.684387141Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.684387141, -28.684387141}
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