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Simplifying 0 = -32x2 + 2025x + 445500 Reorder the terms: 0 = 445500 + 2025x + -32x2 Solving 0 = 445500 + 2025x + -32x2 Solving for variable 'x'. Combine like terms: 0 + -445500 = -445500 -445500 + -2025x + 32x2 = 445500 + 2025x + -32x2 + -445500 + -2025x + 32x2 Reorder the terms: -445500 + -2025x + 32x2 = 445500 + -445500 + 2025x + -2025x + -32x2 + 32x2 Combine like terms: 445500 + -445500 = 0 -445500 + -2025x + 32x2 = 0 + 2025x + -2025x + -32x2 + 32x2 -445500 + -2025x + 32x2 = 2025x + -2025x + -32x2 + 32x2 Combine like terms: 2025x + -2025x = 0 -445500 + -2025x + 32x2 = 0 + -32x2 + 32x2 -445500 + -2025x + 32x2 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 -445500 + -2025x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -13921.875 + -63.28125x + x2 = 0 Move the constant term to the right: Add '13921.875' to each side of the equation. -13921.875 + -63.28125x + 13921.875 + x2 = 0 + 13921.875 Reorder the terms: -13921.875 + 13921.875 + -63.28125x + x2 = 0 + 13921.875 Combine like terms: -13921.875 + 13921.875 = 0.000 0.000 + -63.28125x + x2 = 0 + 13921.875 -63.28125x + x2 = 0 + 13921.875 Combine like terms: 0 + 13921.875 = 13921.875 -63.28125x + x2 = 13921.875 The x term is -63.28125x. Take half its coefficient (-31.640625). Square it (1001.129150) and add it to both sides. Add '1001.129150' to each side of the equation. -63.28125x + 1001.129150 + x2 = 13921.875 + 1001.129150 Reorder the terms: 1001.129150 + -63.28125x + x2 = 13921.875 + 1001.129150 Combine like terms: 13921.875 + 1001.129150 = 14923.00415 1001.129150 + -63.28125x + x2 = 14923.00415 Factor a perfect square on the left side: (x + -31.640625)(x + -31.640625) = 14923.00415 Calculate the square root of the right side: 122.159748485 Break this problem into two subproblems by setting (x + -31.640625) equal to 122.159748485 and -122.159748485.Subproblem 1
x + -31.640625 = 122.159748485 Simplifying x + -31.640625 = 122.159748485 Reorder the terms: -31.640625 + x = 122.159748485 Solving -31.640625 + x = 122.159748485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.640625' to each side of the equation. -31.640625 + 31.640625 + x = 122.159748485 + 31.640625 Combine like terms: -31.640625 + 31.640625 = 0.000000 0.000000 + x = 122.159748485 + 31.640625 x = 122.159748485 + 31.640625 Combine like terms: 122.159748485 + 31.640625 = 153.800373485 x = 153.800373485 Simplifying x = 153.800373485Subproblem 2
x + -31.640625 = -122.159748485 Simplifying x + -31.640625 = -122.159748485 Reorder the terms: -31.640625 + x = -122.159748485 Solving -31.640625 + x = -122.159748485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.640625' to each side of the equation. -31.640625 + 31.640625 + x = -122.159748485 + 31.640625 Combine like terms: -31.640625 + 31.640625 = 0.000000 0.000000 + x = -122.159748485 + 31.640625 x = -122.159748485 + 31.640625 Combine like terms: -122.159748485 + 31.640625 = -90.519123485 x = -90.519123485 Simplifying x = -90.519123485Solution
The solution to the problem is based on the solutions from the subproblems. x = {153.800373485, -90.519123485}
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