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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 = 62.546573405 x = 62.546573405 Simplifying x = 62.546573405Subproblem 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 = 3.453426595 x = 3.453426595 Simplifying x = 3.453426595Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.546573405, 3.453426595}
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