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Simplifying 0.06x + 0.16x(x + 8000) = 2600 Reorder the terms: 0.06x + 0.16x(8000 + x) = 2600 0.06x + (8000 * 0.16x + x * 0.16x) = 2600 0.06x + (1280x + 0.16x2) = 2600 Combine like terms: 0.06x + 1280x = 1280.06x 1280.06x + 0.16x2 = 2600 Solving 1280.06x + 0.16x2 = 2600 Solving for variable 'x'. Reorder the terms: -2600 + 1280.06x + 0.16x2 = 2600 + -2600 Combine like terms: 2600 + -2600 = 0 -2600 + 1280.06x + 0.16x2 = 0 Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. -16250 + 8000.375x + x2 = 0 Move the constant term to the right: Add '16250' to each side of the equation. -16250 + 8000.375x + 16250 + x2 = 0 + 16250 Reorder the terms: -16250 + 16250 + 8000.375x + x2 = 0 + 16250 Combine like terms: -16250 + 16250 = 0 0 + 8000.375x + x2 = 0 + 16250 8000.375x + x2 = 0 + 16250 Combine like terms: 0 + 16250 = 16250 8000.375x + x2 = 16250 The x term is 8000.375x. Take half its coefficient (4000.1875). Square it (16001500.04) and add it to both sides. Add '16001500.04' to each side of the equation. 8000.375x + 16001500.04 + x2 = 16250 + 16001500.04 Reorder the terms: 16001500.04 + 8000.375x + x2 = 16250 + 16001500.04 Combine like terms: 16250 + 16001500.04 = 16017750.04 16001500.04 + 8000.375x + x2 = 16017750.04 Factor a perfect square on the left side: (x + 4000.1875)(x + 4000.1875) = 16017750.04 Calculate the square root of the right side: 4002.218139982 Break this problem into two subproblems by setting (x + 4000.1875) equal to 4002.218139982 and -4002.218139982.Subproblem 1
x + 4000.1875 = 4002.218139982 Simplifying x + 4000.1875 = 4002.218139982 Reorder the terms: 4000.1875 + x = 4002.218139982 Solving 4000.1875 + x = 4002.218139982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4000.1875' to each side of the equation. 4000.1875 + -4000.1875 + x = 4002.218139982 + -4000.1875 Combine like terms: 4000.1875 + -4000.1875 = 0.0000 0.0000 + x = 4002.218139982 + -4000.1875 x = 4002.218139982 + -4000.1875 Combine like terms: 4002.218139982 + -4000.1875 = 2.030639982 x = 2.030639982 Simplifying x = 2.030639982Subproblem 2
x + 4000.1875 = -4002.218139982 Simplifying x + 4000.1875 = -4002.218139982 Reorder the terms: 4000.1875 + x = -4002.218139982 Solving 4000.1875 + x = -4002.218139982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4000.1875' to each side of the equation. 4000.1875 + -4000.1875 + x = -4002.218139982 + -4000.1875 Combine like terms: 4000.1875 + -4000.1875 = 0.0000 0.0000 + x = -4002.218139982 + -4000.1875 x = -4002.218139982 + -4000.1875 Combine like terms: -4002.218139982 + -4000.1875 = -8002.405639982 x = -8002.405639982 Simplifying x = -8002.405639982Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.030639982, -8002.405639982}
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