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Simplifying x(25 + x) + (37 + -1x) = 126 (25 * x + x * x) + (37 + -1x) = 126 (25x + x2) + (37 + -1x) = 126 Remove parenthesis around (37 + -1x) 25x + x2 + 37 + -1x = 126 Reorder the terms: 37 + 25x + -1x + x2 = 126 Combine like terms: 25x + -1x = 24x 37 + 24x + x2 = 126 Solving 37 + 24x + x2 = 126 Solving for variable 'x'. Reorder the terms: 37 + -126 + 24x + x2 = 126 + -126 Combine like terms: 37 + -126 = -89 -89 + 24x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -89 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 24x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + 24x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 24x + x2 = 0 + 89 24x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 24x + x2 = 89 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 89 + 144 Reorder the terms: 144 + 24x + x2 = 89 + 144 Combine like terms: 89 + 144 = 233 144 + 24x + x2 = 233 Factor a perfect square on the left side: (x + 12)(x + 12) = 233 Calculate the square root of the right side: 15.264337522 Break this problem into two subproblems by setting (x + 12) equal to 15.264337522 and -15.264337522.Subproblem 1
x + 12 = 15.264337522 Simplifying x + 12 = 15.264337522 Reorder the terms: 12 + x = 15.264337522 Solving 12 + x = 15.264337522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 15.264337522 + -12 Combine like terms: 12 + -12 = 0 0 + x = 15.264337522 + -12 x = 15.264337522 + -12 Combine like terms: 15.264337522 + -12 = 3.264337522 x = 3.264337522 Simplifying x = 3.264337522Subproblem 2
x + 12 = -15.264337522 Simplifying x + 12 = -15.264337522 Reorder the terms: 12 + x = -15.264337522 Solving 12 + x = -15.264337522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -15.264337522 + -12 Combine like terms: 12 + -12 = 0 0 + x = -15.264337522 + -12 x = -15.264337522 + -12 Combine like terms: -15.264337522 + -12 = -27.264337522 x = -27.264337522 Simplifying x = -27.264337522Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.264337522, -27.264337522}
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