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Simplifying 2x2 + 9x = 3500 Reorder the terms: 9x + 2x2 = 3500 Solving 9x + 2x2 = 3500 Solving for variable 'x'. Reorder the terms: -3500 + 9x + 2x2 = 3500 + -3500 Combine like terms: 3500 + -3500 = 0 -3500 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1750 + 4.5x + x2 = 0 Move the constant term to the right: Add '1750' to each side of the equation. -1750 + 4.5x + 1750 + x2 = 0 + 1750 Reorder the terms: -1750 + 1750 + 4.5x + x2 = 0 + 1750 Combine like terms: -1750 + 1750 = 0 0 + 4.5x + x2 = 0 + 1750 4.5x + x2 = 0 + 1750 Combine like terms: 0 + 1750 = 1750 4.5x + x2 = 1750 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 1750 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 1750 + 5.0625 Combine like terms: 1750 + 5.0625 = 1755.0625 5.0625 + 4.5x + x2 = 1755.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 1755.0625 Calculate the square root of the right side: 41.893466078 Break this problem into two subproblems by setting (x + 2.25) equal to 41.893466078 and -41.893466078.Subproblem 1
x + 2.25 = 41.893466078 Simplifying x + 2.25 = 41.893466078 Reorder the terms: 2.25 + x = 41.893466078 Solving 2.25 + x = 41.893466078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 41.893466078 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 41.893466078 + -2.25 x = 41.893466078 + -2.25 Combine like terms: 41.893466078 + -2.25 = 39.643466078 x = 39.643466078 Simplifying x = 39.643466078Subproblem 2
x + 2.25 = -41.893466078 Simplifying x + 2.25 = -41.893466078 Reorder the terms: 2.25 + x = -41.893466078 Solving 2.25 + x = -41.893466078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -41.893466078 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -41.893466078 + -2.25 x = -41.893466078 + -2.25 Combine like terms: -41.893466078 + -2.25 = -44.143466078 x = -44.143466078 Simplifying x = -44.143466078Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.643466078, -44.143466078}
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