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Simplifying X2 + -6X + 9 = 112 Reorder the terms: 9 + -6X + X2 = 112 Solving 9 + -6X + X2 = 112 Solving for variable 'X'. Reorder the terms: 9 + -112 + -6X + X2 = 112 + -112 Combine like terms: 9 + -112 = -103 -103 + -6X + X2 = 112 + -112 Combine like terms: 112 + -112 = 0 -103 + -6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '103' to each side of the equation. -103 + -6X + 103 + X2 = 0 + 103 Reorder the terms: -103 + 103 + -6X + X2 = 0 + 103 Combine like terms: -103 + 103 = 0 0 + -6X + X2 = 0 + 103 -6X + X2 = 0 + 103 Combine like terms: 0 + 103 = 103 -6X + X2 = 103 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 = 103 + 9 Reorder the terms: 9 + -6X + X2 = 103 + 9 Combine like terms: 103 + 9 = 112 9 + -6X + X2 = 112 Factor a perfect square on the left side: (X + -3)(X + -3) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (X + -3) equal to 10.583005244 and -10.583005244.Subproblem 1
X + -3 = 10.583005244 Simplifying X + -3 = 10.583005244 Reorder the terms: -3 + X = 10.583005244 Solving -3 + X = 10.583005244 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 = 10.583005244 + 3 Combine like terms: -3 + 3 = 0 0 + X = 10.583005244 + 3 X = 10.583005244 + 3 Combine like terms: 10.583005244 + 3 = 13.583005244 X = 13.583005244 Simplifying X = 13.583005244Subproblem 2
X + -3 = -10.583005244 Simplifying X + -3 = -10.583005244 Reorder the terms: -3 + X = -10.583005244 Solving -3 + X = -10.583005244 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 = -10.583005244 + 3 Combine like terms: -3 + 3 = 0 0 + X = -10.583005244 + 3 X = -10.583005244 + 3 Combine like terms: -10.583005244 + 3 = -7.583005244 X = -7.583005244 Simplifying X = -7.583005244Solution
The solution to the problem is based on the solutions from the subproblems. X = {13.583005244, -7.583005244}
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