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Simplifying 0.09x(49000 + x) = 0.02(49000) + 0.03x (49000 * 0.09x + x * 0.09x) = 0.02(49000) + 0.03x (4410x + 0.09x2) = 0.02(49000) + 0.03x Multiply 0.02 * 49000 4410x + 0.09x2 = 980 + 0.03x Solving 4410x + 0.09x2 = 980 + 0.03x Solving for variable 'x'. Reorder the terms: -980 + 4410x + -0.03x + 0.09x2 = 980 + 0.03x + -980 + -0.03x Combine like terms: 4410x + -0.03x = 4409.97x -980 + 4409.97x + 0.09x2 = 980 + 0.03x + -980 + -0.03x Reorder the terms: -980 + 4409.97x + 0.09x2 = 980 + -980 + 0.03x + -0.03x Combine like terms: 980 + -980 = 0 -980 + 4409.97x + 0.09x2 = 0 + 0.03x + -0.03x -980 + 4409.97x + 0.09x2 = 0.03x + -0.03x Combine like terms: 0.03x + -0.03x = 0.00 -980 + 4409.97x + 0.09x2 = 0.00 Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. -10888.88889 + 48999.66667x + x2 = 0 Move the constant term to the right: Add '10888.88889' to each side of the equation. -10888.88889 + 48999.66667x + 10888.88889 + x2 = 0 + 10888.88889 Reorder the terms: -10888.88889 + 10888.88889 + 48999.66667x + x2 = 0 + 10888.88889 Combine like terms: -10888.88889 + 10888.88889 = 0.00000 0.00000 + 48999.66667x + x2 = 0 + 10888.88889 48999.66667x + x2 = 0 + 10888.88889 Combine like terms: 0 + 10888.88889 = 10888.88889 48999.66667x + x2 = 10888.88889 The x term is 48999.66667x. Take half its coefficient (24499.83334). Square it (600241833.7) and add it to both sides. Add '600241833.7' to each side of the equation. 48999.66667x + 600241833.7 + x2 = 10888.88889 + 600241833.7 Reorder the terms: 600241833.7 + 48999.66667x + x2 = 10888.88889 + 600241833.7 Combine like terms: 10888.88889 + 600241833.7 = 600252722.58889 600241833.7 + 48999.66667x + x2 = 600252722.58889 Factor a perfect square on the left side: (x + 24499.83334)(x + 24499.83334) = 600252722.58889 Calculate the square root of the right side: 24500.055562976 Break this problem into two subproblems by setting (x + 24499.83334) equal to 24500.055562976 and -24500.055562976.Subproblem 1
x + 24499.83334 = 24500.055562976 Simplifying x + 24499.83334 = 24500.055562976 Reorder the terms: 24499.83334 + x = 24500.055562976 Solving 24499.83334 + x = 24500.055562976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24499.83334' to each side of the equation. 24499.83334 + -24499.83334 + x = 24500.055562976 + -24499.83334 Combine like terms: 24499.83334 + -24499.83334 = 0.00000 0.00000 + x = 24500.055562976 + -24499.83334 x = 24500.055562976 + -24499.83334 Combine like terms: 24500.055562976 + -24499.83334 = 0.222222976 x = 0.222222976 Simplifying x = 0.222222976Subproblem 2
x + 24499.83334 = -24500.055562976 Simplifying x + 24499.83334 = -24500.055562976 Reorder the terms: 24499.83334 + x = -24500.055562976 Solving 24499.83334 + x = -24500.055562976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24499.83334' to each side of the equation. 24499.83334 + -24499.83334 + x = -24500.055562976 + -24499.83334 Combine like terms: 24499.83334 + -24499.83334 = 0.00000 0.00000 + x = -24500.055562976 + -24499.83334 x = -24500.055562976 + -24499.83334 Combine like terms: -24500.055562976 + -24499.83334 = -48999.888902976 x = -48999.888902976 Simplifying x = -48999.888902976Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.222222976, -48999.888902976}
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