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Simplifying (2.5x2) + 500x + 20000 = 0 Reorder the terms: 20000 + 500x + (2.5x2) = 0 Solving 20000 + 500x + (2.5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 8000 + 200x + x2 = 0 Move the constant term to the right: Add '-8000' to each side of the equation. 8000 + 200x + -8000 + x2 = 0 + -8000 Reorder the terms: 8000 + -8000 + 200x + x2 = 0 + -8000 Combine like terms: 8000 + -8000 = 0 0 + 200x + x2 = 0 + -8000 200x + x2 = 0 + -8000 Combine like terms: 0 + -8000 = -8000 200x + x2 = -8000 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = -8000 + 10000 Reorder the terms: 10000 + 200x + x2 = -8000 + 10000 Combine like terms: -8000 + 10000 = 2000 10000 + 200x + x2 = 2000 Factor a perfect square on the left side: ((x) + 100)((x) + 100) = 2000 Calculate the square root of the right side: 44.72135955 Break this problem into two subproblems by setting ((x) + 100) equal to 44.72135955 and -44.72135955.Subproblem 1
(x) + 100 = 44.72135955 Simplifying (x) + 100 = 44.72135955 x + 100 = 44.72135955 Reorder the terms: 100 + x = 44.72135955 Solving 100 + x = 44.72135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 44.72135955 + -100 Combine like terms: 100 + -100 = 0 0 + x = 44.72135955 + -100 x = 44.72135955 + -100 Combine like terms: 44.72135955 + -100 = -55.27864045 x = -55.27864045 Simplifying x = -55.27864045Subproblem 2
(x) + 100 = -44.72135955 Simplifying (x) + 100 = -44.72135955 x + 100 = -44.72135955 Reorder the terms: 100 + x = -44.72135955 Solving 100 + x = -44.72135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -44.72135955 + -100 Combine like terms: 100 + -100 = 0 0 + x = -44.72135955 + -100 x = -44.72135955 + -100 Combine like terms: -44.72135955 + -100 = -144.72135955 x = -144.72135955 Simplifying x = -144.72135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-55.27864045, -144.72135955}
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