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Simplifying 5x + 8x(2x + 32000) = 31330 Reorder the terms: 5x + 8x(32000 + 2x) = 31330 5x + (32000 * 8x + 2x * 8x) = 31330 5x + (256000x + 16x2) = 31330 Combine like terms: 5x + 256000x = 256005x 256005x + 16x2 = 31330 Solving 256005x + 16x2 = 31330 Solving for variable 'x'. Reorder the terms: -31330 + 256005x + 16x2 = 31330 + -31330 Combine like terms: 31330 + -31330 = 0 -31330 + 256005x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1958.125 + 16000.3125x + x2 = 0 Move the constant term to the right: Add '1958.125' to each side of the equation. -1958.125 + 16000.3125x + 1958.125 + x2 = 0 + 1958.125 Reorder the terms: -1958.125 + 1958.125 + 16000.3125x + x2 = 0 + 1958.125 Combine like terms: -1958.125 + 1958.125 = 0.000 0.000 + 16000.3125x + x2 = 0 + 1958.125 16000.3125x + x2 = 0 + 1958.125 Combine like terms: 0 + 1958.125 = 1958.125 16000.3125x + x2 = 1958.125 The x term is 16000.3125x. Take half its coefficient (8000.15625). Square it (64002500.02) and add it to both sides. Add '64002500.02' to each side of the equation. 16000.3125x + 64002500.02 + x2 = 1958.125 + 64002500.02 Reorder the terms: 64002500.02 + 16000.3125x + x2 = 1958.125 + 64002500.02 Combine like terms: 1958.125 + 64002500.02 = 64004458.145 64002500.02 + 16000.3125x + x2 = 64004458.145 Factor a perfect square on the left side: (x + 8000.15625)(x + 8000.15625) = 64004458.145 Calculate the square root of the right side: 8000.27862921 Break this problem into two subproblems by setting (x + 8000.15625) equal to 8000.27862921 and -8000.27862921.Subproblem 1
x + 8000.15625 = 8000.27862921 Simplifying x + 8000.15625 = 8000.27862921 Reorder the terms: 8000.15625 + x = 8000.27862921 Solving 8000.15625 + x = 8000.27862921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8000.15625' to each side of the equation. 8000.15625 + -8000.15625 + x = 8000.27862921 + -8000.15625 Combine like terms: 8000.15625 + -8000.15625 = 0.00000 0.00000 + x = 8000.27862921 + -8000.15625 x = 8000.27862921 + -8000.15625 Combine like terms: 8000.27862921 + -8000.15625 = 0.12237921 x = 0.12237921 Simplifying x = 0.12237921Subproblem 2
x + 8000.15625 = -8000.27862921 Simplifying x + 8000.15625 = -8000.27862921 Reorder the terms: 8000.15625 + x = -8000.27862921 Solving 8000.15625 + x = -8000.27862921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8000.15625' to each side of the equation. 8000.15625 + -8000.15625 + x = -8000.27862921 + -8000.15625 Combine like terms: 8000.15625 + -8000.15625 = 0.00000 0.00000 + x = -8000.27862921 + -8000.15625 x = -8000.27862921 + -8000.15625 Combine like terms: -8000.27862921 + -8000.15625 = -16000.43487921 x = -16000.43487921 Simplifying x = -16000.43487921Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12237921, -16000.43487921}
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