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Simplifying x(25 + x) + 37 = 126 (25 * x + x * x) + 37 = 126 (25x + x2) + 37 = 126 Reorder the terms: 37 + 25x + x2 = 126 Solving 37 + 25x + x2 = 126 Solving for variable 'x'. Reorder the terms: 37 + -126 + 25x + x2 = 126 + -126 Combine like terms: 37 + -126 = -89 -89 + 25x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -89 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 25x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + 25x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 25x + x2 = 0 + 89 25x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 25x + x2 = 89 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 89 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 89 + 156.25 Combine like terms: 89 + 156.25 = 245.25 156.25 + 25x + x2 = 245.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 245.25 Calculate the square root of the right side: 15.660459763 Break this problem into two subproblems by setting (x + 12.5) equal to 15.660459763 and -15.660459763.Subproblem 1
x + 12.5 = 15.660459763 Simplifying x + 12.5 = 15.660459763 Reorder the terms: 12.5 + x = 15.660459763 Solving 12.5 + x = 15.660459763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 15.660459763 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 15.660459763 + -12.5 x = 15.660459763 + -12.5 Combine like terms: 15.660459763 + -12.5 = 3.160459763 x = 3.160459763 Simplifying x = 3.160459763Subproblem 2
x + 12.5 = -15.660459763 Simplifying x + 12.5 = -15.660459763 Reorder the terms: 12.5 + x = -15.660459763 Solving 12.5 + x = -15.660459763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -15.660459763 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -15.660459763 + -12.5 x = -15.660459763 + -12.5 Combine like terms: -15.660459763 + -12.5 = -28.160459763 x = -28.160459763 Simplifying x = -28.160459763Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.160459763, -28.160459763}
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