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Simplifying 0.125x2 + 30x = 15x + 200 Reorder the terms: 30x + 0.125x2 = 15x + 200 Reorder the terms: 30x + 0.125x2 = 200 + 15x Solving 30x + 0.125x2 = 200 + 15x Solving for variable 'x'. Reorder the terms: -200 + 30x + -15x + 0.125x2 = 200 + 15x + -200 + -15x Combine like terms: 30x + -15x = 15x -200 + 15x + 0.125x2 = 200 + 15x + -200 + -15x Reorder the terms: -200 + 15x + 0.125x2 = 200 + -200 + 15x + -15x Combine like terms: 200 + -200 = 0 -200 + 15x + 0.125x2 = 0 + 15x + -15x -200 + 15x + 0.125x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -200 + 15x + 0.125x2 = 0 Begin completing the square. Divide all terms by 0.125 the coefficient of the squared term: Divide each side by '0.125'. -1600 + 120x + x2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 120x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 120x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 120x + x2 = 0 + 1600 120x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 120x + x2 = 1600 The x term is 120x. Take half its coefficient (60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. 120x + 3600 + x2 = 1600 + 3600 Reorder the terms: 3600 + 120x + x2 = 1600 + 3600 Combine like terms: 1600 + 3600 = 5200 3600 + 120x + x2 = 5200 Factor a perfect square on the left side: (x + 60)(x + 60) = 5200 Calculate the square root of the right side: 72.111025509 Break this problem into two subproblems by setting (x + 60) equal to 72.111025509 and -72.111025509.Subproblem 1
x + 60 = 72.111025509 Simplifying x + 60 = 72.111025509 Reorder the terms: 60 + x = 72.111025509 Solving 60 + x = 72.111025509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + x = 72.111025509 + -60 Combine like terms: 60 + -60 = 0 0 + x = 72.111025509 + -60 x = 72.111025509 + -60 Combine like terms: 72.111025509 + -60 = 12.111025509 x = 12.111025509 Simplifying x = 12.111025509Subproblem 2
x + 60 = -72.111025509 Simplifying x + 60 = -72.111025509 Reorder the terms: 60 + x = -72.111025509 Solving 60 + x = -72.111025509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + x = -72.111025509 + -60 Combine like terms: 60 + -60 = 0 0 + x = -72.111025509 + -60 x = -72.111025509 + -60 Combine like terms: -72.111025509 + -60 = -132.111025509 x = -132.111025509 Simplifying x = -132.111025509Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.111025509, -132.111025509}
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