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Simplifying (X + 1)(X + 2) = 40 Reorder the terms: (1 + X)(X + 2) = 40 Reorder the terms: (1 + X)(2 + X) = 40 Multiply (1 + X) * (2 + X) (1(2 + X) + X(2 + X)) = 40 ((2 * 1 + X * 1) + X(2 + X)) = 40 ((2 + 1X) + X(2 + X)) = 40 (2 + 1X + (2 * X + X * X)) = 40 (2 + 1X + (2X + X2)) = 40 Combine like terms: 1X + 2X = 3X (2 + 3X + X2) = 40 Solving 2 + 3X + X2 = 40 Solving for variable 'X'. Reorder the terms: 2 + -40 + 3X + X2 = 40 + -40 Combine like terms: 2 + -40 = -38 -38 + 3X + X2 = 40 + -40 Combine like terms: 40 + -40 = 0 -38 + 3X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 3X + 38 + X2 = 0 + 38 Reorder the terms: -38 + 38 + 3X + X2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 3X + X2 = 0 + 38 3X + X2 = 0 + 38 Combine like terms: 0 + 38 = 38 3X + X2 = 38 The X term is 3X. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3X + 2.25 + X2 = 38 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 38 + 2.25 Combine like terms: 38 + 2.25 = 40.25 2.25 + 3X + X2 = 40.25 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (X + 1.5) equal to 6.34428877 and -6.34428877.Subproblem 1
X + 1.5 = 6.34428877 Simplifying X + 1.5 = 6.34428877 Reorder the terms: 1.5 + X = 6.34428877 Solving 1.5 + X = 6.34428877 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 6.34428877 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 6.34428877 + -1.5 X = 6.34428877 + -1.5 Combine like terms: 6.34428877 + -1.5 = 4.84428877 X = 4.84428877 Simplifying X = 4.84428877Subproblem 2
X + 1.5 = -6.34428877 Simplifying X + 1.5 = -6.34428877 Reorder the terms: 1.5 + X = -6.34428877 Solving 1.5 + X = -6.34428877 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -6.34428877 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -6.34428877 + -1.5 X = -6.34428877 + -1.5 Combine like terms: -6.34428877 + -1.5 = -7.84428877 X = -7.84428877 Simplifying X = -7.84428877Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.84428877, -7.84428877}
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