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Simplifying x2 + 66x + 216 = 0 Reorder the terms: 216 + 66x + x2 = 0 Solving 216 + 66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-216' to each side of the equation. 216 + 66x + -216 + x2 = 0 + -216 Reorder the terms: 216 + -216 + 66x + x2 = 0 + -216 Combine like terms: 216 + -216 = 0 0 + 66x + x2 = 0 + -216 66x + x2 = 0 + -216 Combine like terms: 0 + -216 = -216 66x + x2 = -216 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 = -216 + 1089 Reorder the terms: 1089 + 66x + x2 = -216 + 1089 Combine like terms: -216 + 1089 = 873 1089 + 66x + x2 = 873 Factor a perfect square on the left side: (x + 33)(x + 33) = 873 Calculate the square root of the right side: 29.546573405 Break this problem into two subproblems by setting (x + 33) equal to 29.546573405 and -29.546573405.Subproblem 1
x + 33 = 29.546573405 Simplifying x + 33 = 29.546573405 Reorder the terms: 33 + x = 29.546573405 Solving 33 + x = 29.546573405 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 = 29.546573405 + -33 Combine like terms: 33 + -33 = 0 0 + x = 29.546573405 + -33 x = 29.546573405 + -33 Combine like terms: 29.546573405 + -33 = -3.453426595 x = -3.453426595 Simplifying x = -3.453426595Subproblem 2
x + 33 = -29.546573405 Simplifying x + 33 = -29.546573405 Reorder the terms: 33 + x = -29.546573405 Solving 33 + x = -29.546573405 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 = -29.546573405 + -33 Combine like terms: 33 + -33 = 0 0 + x = -29.546573405 + -33 x = -29.546573405 + -33 Combine like terms: -29.546573405 + -33 = -62.546573405 x = -62.546573405 Simplifying x = -62.546573405Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.453426595, -62.546573405}
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