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Simplifying x(5 + x) = 10000 (5 * x + x * x) = 10000 (5x + x2) = 10000 Solving 5x + x2 = 10000 Solving for variable 'x'. Reorder the terms: -10000 + 5x + x2 = 10000 + -10000 Combine like terms: 10000 + -10000 = 0 -10000 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 5x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 5x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 5x + x2 = 0 + 10000 5x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 5x + x2 = 10000 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 10000 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 10000 + 6.25 Combine like terms: 10000 + 6.25 = 10006.25 6.25 + 5x + x2 = 10006.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 10006.25 Calculate the square root of the right side: 100.031245119 Break this problem into two subproblems by setting (x + 2.5) equal to 100.031245119 and -100.031245119.Subproblem 1
x + 2.5 = 100.031245119 Simplifying x + 2.5 = 100.031245119 Reorder the terms: 2.5 + x = 100.031245119 Solving 2.5 + x = 100.031245119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 100.031245119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 100.031245119 + -2.5 x = 100.031245119 + -2.5 Combine like terms: 100.031245119 + -2.5 = 97.531245119 x = 97.531245119 Simplifying x = 97.531245119Subproblem 2
x + 2.5 = -100.031245119 Simplifying x + 2.5 = -100.031245119 Reorder the terms: 2.5 + x = -100.031245119 Solving 2.5 + x = -100.031245119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -100.031245119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -100.031245119 + -2.5 x = -100.031245119 + -2.5 Combine like terms: -100.031245119 + -2.5 = -102.531245119 x = -102.531245119 Simplifying x = -102.531245119Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.531245119, -102.531245119}
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