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Simplifying x(25 + x) + (x + -37) = 126 (25 * x + x * x) + (x + -37) = 126 (25x + x2) + (x + -37) = 126 Reorder the terms: 25x + x2 + (-37 + x) = 126 Remove parenthesis around (-37 + x) 25x + x2 + -37 + x = 126 Reorder the terms: -37 + 25x + x + x2 = 126 Combine like terms: 25x + x = 26x -37 + 26x + x2 = 126 Solving -37 + 26x + x2 = 126 Solving for variable 'x'. Reorder the terms: -37 + -126 + 26x + x2 = 126 + -126 Combine like terms: -37 + -126 = -163 -163 + 26x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -163 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '163' to each side of the equation. -163 + 26x + 163 + x2 = 0 + 163 Reorder the terms: -163 + 163 + 26x + x2 = 0 + 163 Combine like terms: -163 + 163 = 0 0 + 26x + x2 = 0 + 163 26x + x2 = 0 + 163 Combine like terms: 0 + 163 = 163 26x + x2 = 163 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 = 163 + 169 Reorder the terms: 169 + 26x + x2 = 163 + 169 Combine like terms: 163 + 169 = 332 169 + 26x + x2 = 332 Factor a perfect square on the left side: (x + 13)(x + 13) = 332 Calculate the square root of the right side: 18.220867158 Break this problem into two subproblems by setting (x + 13) equal to 18.220867158 and -18.220867158.Subproblem 1
x + 13 = 18.220867158 Simplifying x + 13 = 18.220867158 Reorder the terms: 13 + x = 18.220867158 Solving 13 + x = 18.220867158 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 = 18.220867158 + -13 Combine like terms: 13 + -13 = 0 0 + x = 18.220867158 + -13 x = 18.220867158 + -13 Combine like terms: 18.220867158 + -13 = 5.220867158 x = 5.220867158 Simplifying x = 5.220867158Subproblem 2
x + 13 = -18.220867158 Simplifying x + 13 = -18.220867158 Reorder the terms: 13 + x = -18.220867158 Solving 13 + x = -18.220867158 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 = -18.220867158 + -13 Combine like terms: 13 + -13 = 0 0 + x = -18.220867158 + -13 x = -18.220867158 + -13 Combine like terms: -18.220867158 + -13 = -31.220867158 x = -31.220867158 Simplifying x = -31.220867158Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.220867158, -31.220867158}
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