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Simplifying (X + 2)(X + 2) = 9X + 2 Reorder the terms: (2 + X)(X + 2) = 9X + 2 Reorder the terms: (2 + X)(2 + X) = 9X + 2 Multiply (2 + X) * (2 + X) (2(2 + X) + X(2 + X)) = 9X + 2 ((2 * 2 + X * 2) + X(2 + X)) = 9X + 2 ((4 + 2X) + X(2 + X)) = 9X + 2 (4 + 2X + (2 * X + X * X)) = 9X + 2 (4 + 2X + (2X + X2)) = 9X + 2 Combine like terms: 2X + 2X = 4X (4 + 4X + X2) = 9X + 2 Reorder the terms: 4 + 4X + X2 = 2 + 9X Solving 4 + 4X + X2 = 2 + 9X Solving for variable 'X'. Reorder the terms: 4 + -2 + 4X + -9X + X2 = 2 + 9X + -2 + -9X Combine like terms: 4 + -2 = 2 2 + 4X + -9X + X2 = 2 + 9X + -2 + -9X Combine like terms: 4X + -9X = -5X 2 + -5X + X2 = 2 + 9X + -2 + -9X Reorder the terms: 2 + -5X + X2 = 2 + -2 + 9X + -9X Combine like terms: 2 + -2 = 0 2 + -5X + X2 = 0 + 9X + -9X 2 + -5X + X2 = 9X + -9X Combine like terms: 9X + -9X = 0 2 + -5X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5X + -2 + X2 = 0 + -2 Reorder the terms: 2 + -2 + -5X + X2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5X + X2 = 0 + -2 -5X + X2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5X + X2 = -2 The X term is -5X. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5X + 6.25 + X2 = -2 + 6.25 Reorder the terms: 6.25 + -5X + X2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + -5X + X2 = 4.25 Factor a perfect square on the left side: (X + -2.5)(X + -2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (X + -2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
X + -2.5 = 2.061552813 Simplifying X + -2.5 = 2.061552813 Reorder the terms: -2.5 + X = 2.061552813 Solving -2.5 + X = 2.061552813 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = 2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = 2.061552813 + 2.5 X = 2.061552813 + 2.5 Combine like terms: 2.061552813 + 2.5 = 4.561552813 X = 4.561552813 Simplifying X = 4.561552813Subproblem 2
X + -2.5 = -2.061552813 Simplifying X + -2.5 = -2.061552813 Reorder the terms: -2.5 + X = -2.061552813 Solving -2.5 + X = -2.061552813 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = -2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = -2.061552813 + 2.5 X = -2.061552813 + 2.5 Combine like terms: -2.061552813 + 2.5 = 0.438447187 X = 0.438447187 Simplifying X = 0.438447187Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.561552813, 0.438447187}
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