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Simplifying (2x + 5)(x) = 360 Reorder the terms: (5 + 2x)(x) = 360 Reorder the terms for easier multiplication: x(5 + 2x) = 360 (5 * x + 2x * x) = 360 (5x + 2x2) = 360 Solving 5x + 2x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 5x + 2x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -180 + 2.5x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 2.5x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 2.5x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 2.5x + x2 = 0 + 180 2.5x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 2.5x + x2 = 180 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 180 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 180 + 1.5625 Combine like terms: 180 + 1.5625 = 181.5625 1.5625 + 2.5x + x2 = 181.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 181.5625 Calculate the square root of the right side: 13.474512978 Break this problem into two subproblems by setting (x + 1.25) equal to 13.474512978 and -13.474512978.Subproblem 1
x + 1.25 = 13.474512978 Simplifying x + 1.25 = 13.474512978 Reorder the terms: 1.25 + x = 13.474512978 Solving 1.25 + x = 13.474512978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 13.474512978 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 13.474512978 + -1.25 x = 13.474512978 + -1.25 Combine like terms: 13.474512978 + -1.25 = 12.224512978 x = 12.224512978 Simplifying x = 12.224512978Subproblem 2
x + 1.25 = -13.474512978 Simplifying x + 1.25 = -13.474512978 Reorder the terms: 1.25 + x = -13.474512978 Solving 1.25 + x = -13.474512978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -13.474512978 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -13.474512978 + -1.25 x = -13.474512978 + -1.25 Combine like terms: -13.474512978 + -1.25 = -14.724512978 x = -14.724512978 Simplifying x = -14.724512978Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.224512978, -14.724512978}
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