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Simplifying (X2 + -6X) + 55 = 180 Reorder the terms: (-6X + X2) + 55 = 180 Remove parenthesis around (-6X + X2) -6X + X2 + 55 = 180 Reorder the terms: 55 + -6X + X2 = 180 Solving 55 + -6X + X2 = 180 Solving for variable 'X'. Reorder the terms: 55 + -180 + -6X + X2 = 180 + -180 Combine like terms: 55 + -180 = -125 -125 + -6X + X2 = 180 + -180 Combine like terms: 180 + -180 = 0 -125 + -6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -6X + 125 + X2 = 0 + 125 Reorder the terms: -125 + 125 + -6X + X2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -6X + X2 = 0 + 125 -6X + X2 = 0 + 125 Combine like terms: 0 + 125 = 125 -6X + X2 = 125 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 125 + 9 Reorder the terms: 9 + -6X + X2 = 125 + 9 Combine like terms: 125 + 9 = 134 9 + -6X + X2 = 134 Factor a perfect square on the left side: (X + -3)(X + -3) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (X + -3) equal to 11.575836903 and -11.575836903.Subproblem 1
X + -3 = 11.575836903 Simplifying X + -3 = 11.575836903 Reorder the terms: -3 + X = 11.575836903 Solving -3 + X = 11.575836903 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 11.575836903 + 3 Combine like terms: -3 + 3 = 0 0 + X = 11.575836903 + 3 X = 11.575836903 + 3 Combine like terms: 11.575836903 + 3 = 14.575836903 X = 14.575836903 Simplifying X = 14.575836903Subproblem 2
X + -3 = -11.575836903 Simplifying X + -3 = -11.575836903 Reorder the terms: -3 + X = -11.575836903 Solving -3 + X = -11.575836903 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -11.575836903 + 3 Combine like terms: -3 + 3 = 0 0 + X = -11.575836903 + 3 X = -11.575836903 + 3 Combine like terms: -11.575836903 + 3 = -8.575836903 X = -8.575836903 Simplifying X = -8.575836903Solution
The solution to the problem is based on the solutions from the subproblems. X = {14.575836903, -8.575836903}
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