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Simplifying (x + 20)(x + 30) = 5000 Reorder the terms: (20 + x)(x + 30) = 5000 Reorder the terms: (20 + x)(30 + x) = 5000 Multiply (20 + x) * (30 + x) (20(30 + x) + x(30 + x)) = 5000 ((30 * 20 + x * 20) + x(30 + x)) = 5000 ((600 + 20x) + x(30 + x)) = 5000 (600 + 20x + (30 * x + x * x)) = 5000 (600 + 20x + (30x + x2)) = 5000 Combine like terms: 20x + 30x = 50x (600 + 50x + x2) = 5000 Solving 600 + 50x + x2 = 5000 Solving for variable 'x'. Reorder the terms: 600 + -5000 + 50x + x2 = 5000 + -5000 Combine like terms: 600 + -5000 = -4400 -4400 + 50x + x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -4400 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4400' to each side of the equation. -4400 + 50x + 4400 + x2 = 0 + 4400 Reorder the terms: -4400 + 4400 + 50x + x2 = 0 + 4400 Combine like terms: -4400 + 4400 = 0 0 + 50x + x2 = 0 + 4400 50x + x2 = 0 + 4400 Combine like terms: 0 + 4400 = 4400 50x + x2 = 4400 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 4400 + 625 Reorder the terms: 625 + 50x + x2 = 4400 + 625 Combine like terms: 4400 + 625 = 5025 625 + 50x + x2 = 5025 Factor a perfect square on the left side: (x + 25)(x + 25) = 5025 Calculate the square root of the right side: 70.887234394 Break this problem into two subproblems by setting (x + 25) equal to 70.887234394 and -70.887234394.Subproblem 1
x + 25 = 70.887234394 Simplifying x + 25 = 70.887234394 Reorder the terms: 25 + x = 70.887234394 Solving 25 + x = 70.887234394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 70.887234394 + -25 Combine like terms: 25 + -25 = 0 0 + x = 70.887234394 + -25 x = 70.887234394 + -25 Combine like terms: 70.887234394 + -25 = 45.887234394 x = 45.887234394 Simplifying x = 45.887234394Subproblem 2
x + 25 = -70.887234394 Simplifying x + 25 = -70.887234394 Reorder the terms: 25 + x = -70.887234394 Solving 25 + x = -70.887234394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -70.887234394 + -25 Combine like terms: 25 + -25 = 0 0 + x = -70.887234394 + -25 x = -70.887234394 + -25 Combine like terms: -70.887234394 + -25 = -95.887234394 x = -95.887234394 Simplifying x = -95.887234394Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.887234394, -95.887234394}
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