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Simplifying x(57 + 5)(52 + -2x) = 1500 Combine like terms: 57 + 5 = 62 x(62)(52 + -2x) = 1500 Reorder the terms for easier multiplication: 62x(52 + -2x) = 1500 (52 * 62x + -2x * 62x) = 1500 (3224x + -124x2) = 1500 Solving 3224x + -124x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 3224x + -124x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 3224x + -124x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-375 + 806x + -31x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-375 + 806x + -31x2)' equal to zero and attempt to solve: Simplifying -375 + 806x + -31x2 = 0 Solving -375 + 806x + -31x2 = 0 Begin completing the square. Divide all terms by -31 the coefficient of the squared term: Divide each side by '-31'. 12.09677419 + -26x + x2 = 0 Move the constant term to the right: Add '-12.09677419' to each side of the equation. 12.09677419 + -26x + -12.09677419 + x2 = 0 + -12.09677419 Reorder the terms: 12.09677419 + -12.09677419 + -26x + x2 = 0 + -12.09677419 Combine like terms: 12.09677419 + -12.09677419 = 0.00000000 0.00000000 + -26x + x2 = 0 + -12.09677419 -26x + x2 = 0 + -12.09677419 Combine like terms: 0 + -12.09677419 = -12.09677419 -26x + x2 = -12.09677419 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -12.09677419 + 169 Reorder the terms: 169 + -26x + x2 = -12.09677419 + 169 Combine like terms: -12.09677419 + 169 = 156.90322581 169 + -26x + x2 = 156.90322581 Factor a perfect square on the left side: (x + -13)(x + -13) = 156.90322581 Calculate the square root of the right side: 12.52610178 Break this problem into two subproblems by setting (x + -13) equal to 12.52610178 and -12.52610178.Subproblem 1
x + -13 = 12.52610178 Simplifying x + -13 = 12.52610178 Reorder the terms: -13 + x = 12.52610178 Solving -13 + x = 12.52610178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 12.52610178 + 13 Combine like terms: -13 + 13 = 0 0 + x = 12.52610178 + 13 x = 12.52610178 + 13 Combine like terms: 12.52610178 + 13 = 25.52610178 x = 25.52610178 Simplifying x = 25.52610178Subproblem 2
x + -13 = -12.52610178 Simplifying x + -13 = -12.52610178 Reorder the terms: -13 + x = -12.52610178 Solving -13 + x = -12.52610178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -12.52610178 + 13 Combine like terms: -13 + 13 = 0 0 + x = -12.52610178 + 13 x = -12.52610178 + 13 Combine like terms: -12.52610178 + 13 = 0.47389822 x = 0.47389822 Simplifying x = 0.47389822Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.52610178, 0.47389822}Solution
x = {25.52610178, 0.47389822}
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