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Simplifying 0.85x * 2000 * 20(1436 + -0.425x) = 2654000000 Reorder the terms for easier multiplication: 0.85 * 2000 * 20x(1436 + -0.425x) = 2654000000 Multiply 0.85 * 2000 1700 * 20x(1436 + -0.425x) = 2654000000 Multiply 1700 * 20 34000x(1436 + -0.425x) = 2654000000 (1436 * 34000x + -0.425x * 34000x) = 2654000000 (48824000x + -14450x2) = 2654000000 Solving 48824000x + -14450x2 = 2654000000 Solving for variable 'x'. Reorder the terms: -2654000000 + 48824000x + -14450x2 = 2654000000 + -2654000000 Combine like terms: 2654000000 + -2654000000 = 0 -2654000000 + 48824000x + -14450x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-53080000 + 976480x + -289x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-53080000 + 976480x + -289x2)' equal to zero and attempt to solve: Simplifying -53080000 + 976480x + -289x2 = 0 Solving -53080000 + 976480x + -289x2 = 0 Begin completing the square. Divide all terms by -289 the coefficient of the squared term: Divide each side by '-289'. 183667.8201 + -3378.823529x + x2 = 0 Move the constant term to the right: Add '-183667.8201' to each side of the equation. 183667.8201 + -3378.823529x + -183667.8201 + x2 = 0 + -183667.8201 Reorder the terms: 183667.8201 + -183667.8201 + -3378.823529x + x2 = 0 + -183667.8201 Combine like terms: 183667.8201 + -183667.8201 = 0.0000 0.0000 + -3378.823529x + x2 = 0 + -183667.8201 -3378.823529x + x2 = 0 + -183667.8201 Combine like terms: 0 + -183667.8201 = -183667.8201 -3378.823529x + x2 = -183667.8201 The x term is -3378.823529x. Take half its coefficient (-1689.411765). Square it (2854112.112) and add it to both sides. Add '2854112.112' to each side of the equation. -3378.823529x + 2854112.112 + x2 = -183667.8201 + 2854112.112 Reorder the terms: 2854112.112 + -3378.823529x + x2 = -183667.8201 + 2854112.112 Combine like terms: -183667.8201 + 2854112.112 = 2670444.2919 2854112.112 + -3378.823529x + x2 = 2670444.2919 Factor a perfect square on the left side: (x + -1689.411765)(x + -1689.411765) = 2670444.2919 Calculate the square root of the right side: 1634.149409295 Break this problem into two subproblems by setting (x + -1689.411765) equal to 1634.149409295 and -1634.149409295.Subproblem 1
x + -1689.411765 = 1634.149409295 Simplifying x + -1689.411765 = 1634.149409295 Reorder the terms: -1689.411765 + x = 1634.149409295 Solving -1689.411765 + x = 1634.149409295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1689.411765' to each side of the equation. -1689.411765 + 1689.411765 + x = 1634.149409295 + 1689.411765 Combine like terms: -1689.411765 + 1689.411765 = 0.000000 0.000000 + x = 1634.149409295 + 1689.411765 x = 1634.149409295 + 1689.411765 Combine like terms: 1634.149409295 + 1689.411765 = 3323.561174295 x = 3323.561174295 Simplifying x = 3323.561174295Subproblem 2
x + -1689.411765 = -1634.149409295 Simplifying x + -1689.411765 = -1634.149409295 Reorder the terms: -1689.411765 + x = -1634.149409295 Solving -1689.411765 + x = -1634.149409295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1689.411765' to each side of the equation. -1689.411765 + 1689.411765 + x = -1634.149409295 + 1689.411765 Combine like terms: -1689.411765 + 1689.411765 = 0.000000 0.000000 + x = -1634.149409295 + 1689.411765 x = -1634.149409295 + 1689.411765 Combine like terms: -1634.149409295 + 1689.411765 = 55.262355705 x = 55.262355705 Simplifying x = 55.262355705Solution
The solution to the problem is based on the solutions from the subproblems. x = {3323.561174295, 55.262355705}Solution
x = {3323.561174295, 55.262355705}
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