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Simplifying 33x(x + 6) = 8320 Reorder the terms: 33x(6 + x) = 8320 (6 * 33x + x * 33x) = 8320 (198x + 33x2) = 8320 Solving 198x + 33x2 = 8320 Solving for variable 'x'. Reorder the terms: -8320 + 198x + 33x2 = 8320 + -8320 Combine like terms: 8320 + -8320 = 0 -8320 + 198x + 33x2 = 0 Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. -252.1212121 + 6x + x2 = 0 Move the constant term to the right: Add '252.1212121' to each side of the equation. -252.1212121 + 6x + 252.1212121 + x2 = 0 + 252.1212121 Reorder the terms: -252.1212121 + 252.1212121 + 6x + x2 = 0 + 252.1212121 Combine like terms: -252.1212121 + 252.1212121 = 0.0000000 0.0000000 + 6x + x2 = 0 + 252.1212121 6x + x2 = 0 + 252.1212121 Combine like terms: 0 + 252.1212121 = 252.1212121 6x + x2 = 252.1212121 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 252.1212121 + 9 Reorder the terms: 9 + 6x + x2 = 252.1212121 + 9 Combine like terms: 252.1212121 + 9 = 261.1212121 9 + 6x + x2 = 261.1212121 Factor a perfect square on the left side: (x + 3)(x + 3) = 261.1212121 Calculate the square root of the right side: 16.159245406 Break this problem into two subproblems by setting (x + 3) equal to 16.159245406 and -16.159245406.Subproblem 1
x + 3 = 16.159245406 Simplifying x + 3 = 16.159245406 Reorder the terms: 3 + x = 16.159245406 Solving 3 + x = 16.159245406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 16.159245406 + -3 Combine like terms: 3 + -3 = 0 0 + x = 16.159245406 + -3 x = 16.159245406 + -3 Combine like terms: 16.159245406 + -3 = 13.159245406 x = 13.159245406 Simplifying x = 13.159245406Subproblem 2
x + 3 = -16.159245406 Simplifying x + 3 = -16.159245406 Reorder the terms: 3 + x = -16.159245406 Solving 3 + x = -16.159245406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -16.159245406 + -3 Combine like terms: 3 + -3 = 0 0 + x = -16.159245406 + -3 x = -16.159245406 + -3 Combine like terms: -16.159245406 + -3 = -19.159245406 x = -19.159245406 Simplifying x = -19.159245406Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.159245406, -19.159245406}
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