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Simplifying -5x2 + -330x + 3300 = 0 Reorder the terms: 3300 + -330x + -5x2 = 0 Solving 3300 + -330x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(660 + -66x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(660 + -66x + -1x2)' equal to zero and attempt to solve: Simplifying 660 + -66x + -1x2 = 0 Solving 660 + -66x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -660 + 66x + x2 = 0 Move the constant term to the right: Add '660' to each side of the equation. -660 + 66x + 660 + x2 = 0 + 660 Reorder the terms: -660 + 660 + 66x + x2 = 0 + 660 Combine like terms: -660 + 660 = 0 0 + 66x + x2 = 0 + 660 66x + x2 = 0 + 660 Combine like terms: 0 + 660 = 660 66x + x2 = 660 The x term is 66x. Take half its coefficient (33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. 66x + 1089 + x2 = 660 + 1089 Reorder the terms: 1089 + 66x + x2 = 660 + 1089 Combine like terms: 660 + 1089 = 1749 1089 + 66x + x2 = 1749 Factor a perfect square on the left side: (x + 33)(x + 33) = 1749 Calculate the square root of the right side: 41.821047333 Break this problem into two subproblems by setting (x + 33) equal to 41.821047333 and -41.821047333.Subproblem 1
x + 33 = 41.821047333 Simplifying x + 33 = 41.821047333 Reorder the terms: 33 + x = 41.821047333 Solving 33 + x = 41.821047333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + x = 41.821047333 + -33 Combine like terms: 33 + -33 = 0 0 + x = 41.821047333 + -33 x = 41.821047333 + -33 Combine like terms: 41.821047333 + -33 = 8.821047333 x = 8.821047333 Simplifying x = 8.821047333Subproblem 2
x + 33 = -41.821047333 Simplifying x + 33 = -41.821047333 Reorder the terms: 33 + x = -41.821047333 Solving 33 + x = -41.821047333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + x = -41.821047333 + -33 Combine like terms: 33 + -33 = 0 0 + x = -41.821047333 + -33 x = -41.821047333 + -33 Combine like terms: -41.821047333 + -33 = -74.821047333 x = -74.821047333 Simplifying x = -74.821047333Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.821047333, -74.821047333}Solution
x = {8.821047333, -74.821047333}
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