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Simplifying (x + 50)(x + 5) = 49 Reorder the terms: (50 + x)(x + 5) = 49 Reorder the terms: (50 + x)(5 + x) = 49 Multiply (50 + x) * (5 + x) (50(5 + x) + x(5 + x)) = 49 ((5 * 50 + x * 50) + x(5 + x)) = 49 ((250 + 50x) + x(5 + x)) = 49 (250 + 50x + (5 * x + x * x)) = 49 (250 + 50x + (5x + x2)) = 49 Combine like terms: 50x + 5x = 55x (250 + 55x + x2) = 49 Solving 250 + 55x + x2 = 49 Solving for variable 'x'. Reorder the terms: 250 + -49 + 55x + x2 = 49 + -49 Combine like terms: 250 + -49 = 201 201 + 55x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 201 + 55x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-201' to each side of the equation. 201 + 55x + -201 + x2 = 0 + -201 Reorder the terms: 201 + -201 + 55x + x2 = 0 + -201 Combine like terms: 201 + -201 = 0 0 + 55x + x2 = 0 + -201 55x + x2 = 0 + -201 Combine like terms: 0 + -201 = -201 55x + x2 = -201 The x term is 55x. Take half its coefficient (27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. 55x + 756.25 + x2 = -201 + 756.25 Reorder the terms: 756.25 + 55x + x2 = -201 + 756.25 Combine like terms: -201 + 756.25 = 555.25 756.25 + 55x + x2 = 555.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 555.25 Calculate the square root of the right side: 23.563743336 Break this problem into two subproblems by setting (x + 27.5) equal to 23.563743336 and -23.563743336.Subproblem 1
x + 27.5 = 23.563743336 Simplifying x + 27.5 = 23.563743336 Reorder the terms: 27.5 + x = 23.563743336 Solving 27.5 + x = 23.563743336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 23.563743336 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 23.563743336 + -27.5 x = 23.563743336 + -27.5 Combine like terms: 23.563743336 + -27.5 = -3.936256664 x = -3.936256664 Simplifying x = -3.936256664Subproblem 2
x + 27.5 = -23.563743336 Simplifying x + 27.5 = -23.563743336 Reorder the terms: 27.5 + x = -23.563743336 Solving 27.5 + x = -23.563743336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -23.563743336 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -23.563743336 + -27.5 x = -23.563743336 + -27.5 Combine like terms: -23.563743336 + -27.5 = -51.063743336 x = -51.063743336 Simplifying x = -51.063743336Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.936256664, -51.063743336}
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