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Simplifying 2X + 2 = X2 + -4X + 4 Reorder the terms: 2 + 2X = X2 + -4X + 4 Reorder the terms: 2 + 2X = 4 + -4X + X2 Solving 2 + 2X = 4 + -4X + X2 Solving for variable 'X'. Reorder the terms: 2 + -4 + 2X + 4X + -1X2 = 4 + -4X + X2 + -4 + 4X + -1X2 Combine like terms: 2 + -4 = -2 -2 + 2X + 4X + -1X2 = 4 + -4X + X2 + -4 + 4X + -1X2 Combine like terms: 2X + 4X = 6X -2 + 6X + -1X2 = 4 + -4X + X2 + -4 + 4X + -1X2 Reorder the terms: -2 + 6X + -1X2 = 4 + -4 + -4X + 4X + X2 + -1X2 Combine like terms: 4 + -4 = 0 -2 + 6X + -1X2 = 0 + -4X + 4X + X2 + -1X2 -2 + 6X + -1X2 = -4X + 4X + X2 + -1X2 Combine like terms: -4X + 4X = 0 -2 + 6X + -1X2 = 0 + X2 + -1X2 -2 + 6X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -2 + 6X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -6X + X2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6X + -2 + X2 = 0 + -2 Reorder the terms: 2 + -2 + -6X + X2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6X + X2 = 0 + -2 -6X + X2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6X + X2 = -2 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 = -2 + 9 Reorder the terms: 9 + -6X + X2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6X + X2 = 7 Factor a perfect square on the left side: (X + -3)(X + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (X + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
X + -3 = 2.645751311 Simplifying X + -3 = 2.645751311 Reorder the terms: -3 + X = 2.645751311 Solving -3 + X = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + X = 2.645751311 + 3 X = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 X = 5.645751311 Simplifying X = 5.645751311Subproblem 2
X + -3 = -2.645751311 Simplifying X + -3 = -2.645751311 Reorder the terms: -3 + X = -2.645751311 Solving -3 + X = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + X = -2.645751311 + 3 X = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 X = 0.354248689 Simplifying X = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.645751311, 0.354248689}
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