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Simplifying x2 + -120x + -3276 = 0 Reorder the terms: -3276 + -120x + x2 = 0 Solving -3276 + -120x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3276' to each side of the equation. -3276 + -120x + 3276 + x2 = 0 + 3276 Reorder the terms: -3276 + 3276 + -120x + x2 = 0 + 3276 Combine like terms: -3276 + 3276 = 0 0 + -120x + x2 = 0 + 3276 -120x + x2 = 0 + 3276 Combine like terms: 0 + 3276 = 3276 -120x + x2 = 3276 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = 3276 + 3600 Reorder the terms: 3600 + -120x + x2 = 3276 + 3600 Combine like terms: 3276 + 3600 = 6876 3600 + -120x + x2 = 6876 Factor a perfect square on the left side: (x + -60)(x + -60) = 6876 Calculate the square root of the right side: 82.921649767 Break this problem into two subproblems by setting (x + -60) equal to 82.921649767 and -82.921649767.Subproblem 1
x + -60 = 82.921649767 Simplifying x + -60 = 82.921649767 Reorder the terms: -60 + x = 82.921649767 Solving -60 + x = 82.921649767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 82.921649767 + 60 Combine like terms: -60 + 60 = 0 0 + x = 82.921649767 + 60 x = 82.921649767 + 60 Combine like terms: 82.921649767 + 60 = 142.921649767 x = 142.921649767 Simplifying x = 142.921649767Subproblem 2
x + -60 = -82.921649767 Simplifying x + -60 = -82.921649767 Reorder the terms: -60 + x = -82.921649767 Solving -60 + x = -82.921649767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -82.921649767 + 60 Combine like terms: -60 + 60 = 0 0 + x = -82.921649767 + 60 x = -82.921649767 + 60 Combine like terms: -82.921649767 + 60 = -22.921649767 x = -22.921649767 Simplifying x = -22.921649767Solution
The solution to the problem is based on the solutions from the subproblems. x = {142.921649767, -22.921649767}
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