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Simplifying x2 + 66x + -1 = 0 Reorder the terms: -1 + 66x + x2 = 0 Solving -1 + 66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 66x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 66x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 66x + x2 = 0 + 1 66x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 66x + x2 = 1 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 = 1 + 1089 Reorder the terms: 1089 + 66x + x2 = 1 + 1089 Combine like terms: 1 + 1089 = 1090 1089 + 66x + x2 = 1090 Factor a perfect square on the left side: (x + 33)(x + 33) = 1090 Calculate the square root of the right side: 33.015148038 Break this problem into two subproblems by setting (x + 33) equal to 33.015148038 and -33.015148038.Subproblem 1
x + 33 = 33.015148038 Simplifying x + 33 = 33.015148038 Reorder the terms: 33 + x = 33.015148038 Solving 33 + x = 33.015148038 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 = 33.015148038 + -33 Combine like terms: 33 + -33 = 0 0 + x = 33.015148038 + -33 x = 33.015148038 + -33 Combine like terms: 33.015148038 + -33 = 0.015148038 x = 0.015148038 Simplifying x = 0.015148038Subproblem 2
x + 33 = -33.015148038 Simplifying x + 33 = -33.015148038 Reorder the terms: 33 + x = -33.015148038 Solving 33 + x = -33.015148038 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 = -33.015148038 + -33 Combine like terms: 33 + -33 = 0 0 + x = -33.015148038 + -33 x = -33.015148038 + -33 Combine like terms: -33.015148038 + -33 = -66.015148038 x = -66.015148038 Simplifying x = -66.015148038Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.015148038, -66.015148038}
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