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Simplifying x2 + -12x + -92 = 0 Reorder the terms: -92 + -12x + x2 = 0 Solving -92 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + -12x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + -12x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + -12x + x2 = 0 + 92 -12x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 -12x + x2 = 92 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 92 + 36 Reorder the terms: 36 + -12x + x2 = 92 + 36 Combine like terms: 92 + 36 = 128 36 + -12x + x2 = 128 Factor a perfect square on the left side: (x + -6)(x + -6) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + -6) equal to 11.313708499 and -11.313708499.Subproblem 1
x + -6 = 11.313708499 Simplifying x + -6 = 11.313708499 Reorder the terms: -6 + x = 11.313708499 Solving -6 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 11.313708499 + 6 Combine like terms: -6 + 6 = 0 0 + x = 11.313708499 + 6 x = 11.313708499 + 6 Combine like terms: 11.313708499 + 6 = 17.313708499 x = 17.313708499 Simplifying x = 17.313708499Subproblem 2
x + -6 = -11.313708499 Simplifying x + -6 = -11.313708499 Reorder the terms: -6 + x = -11.313708499 Solving -6 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -11.313708499 + 6 Combine like terms: -6 + 6 = 0 0 + x = -11.313708499 + 6 x = -11.313708499 + 6 Combine like terms: -11.313708499 + 6 = -5.313708499 x = -5.313708499 Simplifying x = -5.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.313708499, -5.313708499}
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