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Simplifying 50x + 2x2 = 1427 Solving 50x + 2x2 = 1427 Solving for variable 'x'. Reorder the terms: -1427 + 50x + 2x2 = 1427 + -1427 Combine like terms: 1427 + -1427 = 0 -1427 + 50x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -713.5 + 25x + x2 = 0 Move the constant term to the right: Add '713.5' to each side of the equation. -713.5 + 25x + 713.5 + x2 = 0 + 713.5 Reorder the terms: -713.5 + 713.5 + 25x + x2 = 0 + 713.5 Combine like terms: -713.5 + 713.5 = 0.0 0.0 + 25x + x2 = 0 + 713.5 25x + x2 = 0 + 713.5 Combine like terms: 0 + 713.5 = 713.5 25x + x2 = 713.5 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 = 713.5 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 713.5 + 156.25 Combine like terms: 713.5 + 156.25 = 869.75 156.25 + 25x + x2 = 869.75 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 869.75 Calculate the square root of the right side: 29.491524206 Break this problem into two subproblems by setting (x + 12.5) equal to 29.491524206 and -29.491524206.Subproblem 1
x + 12.5 = 29.491524206 Simplifying x + 12.5 = 29.491524206 Reorder the terms: 12.5 + x = 29.491524206 Solving 12.5 + x = 29.491524206 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 = 29.491524206 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 29.491524206 + -12.5 x = 29.491524206 + -12.5 Combine like terms: 29.491524206 + -12.5 = 16.991524206 x = 16.991524206 Simplifying x = 16.991524206Subproblem 2
x + 12.5 = -29.491524206 Simplifying x + 12.5 = -29.491524206 Reorder the terms: 12.5 + x = -29.491524206 Solving 12.5 + x = -29.491524206 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 = -29.491524206 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -29.491524206 + -12.5 x = -29.491524206 + -12.5 Combine like terms: -29.491524206 + -12.5 = -41.991524206 x = -41.991524206 Simplifying x = -41.991524206Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.991524206, -41.991524206}
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