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Simplifying x2 + 66x + -528 = 0 Reorder the terms: -528 + 66x + x2 = 0 Solving -528 + 66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '528' to each side of the equation. -528 + 66x + 528 + x2 = 0 + 528 Reorder the terms: -528 + 528 + 66x + x2 = 0 + 528 Combine like terms: -528 + 528 = 0 0 + 66x + x2 = 0 + 528 66x + x2 = 0 + 528 Combine like terms: 0 + 528 = 528 66x + x2 = 528 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 = 528 + 1089 Reorder the terms: 1089 + 66x + x2 = 528 + 1089 Combine like terms: 528 + 1089 = 1617 1089 + 66x + x2 = 1617 Factor a perfect square on the left side: (x + 33)(x + 33) = 1617 Calculate the square root of the right side: 40.211938526 Break this problem into two subproblems by setting (x + 33) equal to 40.211938526 and -40.211938526.Subproblem 1
x + 33 = 40.211938526 Simplifying x + 33 = 40.211938526 Reorder the terms: 33 + x = 40.211938526 Solving 33 + x = 40.211938526 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 = 40.211938526 + -33 Combine like terms: 33 + -33 = 0 0 + x = 40.211938526 + -33 x = 40.211938526 + -33 Combine like terms: 40.211938526 + -33 = 7.211938526 x = 7.211938526 Simplifying x = 7.211938526Subproblem 2
x + 33 = -40.211938526 Simplifying x + 33 = -40.211938526 Reorder the terms: 33 + x = -40.211938526 Solving 33 + x = -40.211938526 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 = -40.211938526 + -33 Combine like terms: 33 + -33 = 0 0 + x = -40.211938526 + -33 x = -40.211938526 + -33 Combine like terms: -40.211938526 + -33 = -73.211938526 x = -73.211938526 Simplifying x = -73.211938526Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.211938526, -73.211938526}
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