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Simplifying 50 + x(75 + 2x) = 0 50 + (75 * x + 2x * x) = 0 50 + (75x + 2x2) = 0 Solving 50 + 75x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25 + 37.5x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + 37.5x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 37.5x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 37.5x + x2 = 0 + -25 37.5x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 37.5x + x2 = -25 The x term is 37.5x. Take half its coefficient (18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. 37.5x + 351.5625 + x2 = -25 + 351.5625 Reorder the terms: 351.5625 + 37.5x + x2 = -25 + 351.5625 Combine like terms: -25 + 351.5625 = 326.5625 351.5625 + 37.5x + x2 = 326.5625 Factor a perfect square on the left side: (x + 18.75)(x + 18.75) = 326.5625 Calculate the square root of the right side: 18.071040369 Break this problem into two subproblems by setting (x + 18.75) equal to 18.071040369 and -18.071040369.Subproblem 1
x + 18.75 = 18.071040369 Simplifying x + 18.75 = 18.071040369 Reorder the terms: 18.75 + x = 18.071040369 Solving 18.75 + x = 18.071040369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = 18.071040369 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = 18.071040369 + -18.75 x = 18.071040369 + -18.75 Combine like terms: 18.071040369 + -18.75 = -0.678959631 x = -0.678959631 Simplifying x = -0.678959631Subproblem 2
x + 18.75 = -18.071040369 Simplifying x + 18.75 = -18.071040369 Reorder the terms: 18.75 + x = -18.071040369 Solving 18.75 + x = -18.071040369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = -18.071040369 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = -18.071040369 + -18.75 x = -18.071040369 + -18.75 Combine like terms: -18.071040369 + -18.75 = -36.821040369 x = -36.821040369 Simplifying x = -36.821040369Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.678959631, -36.821040369}
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