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Simplifying (x + 1)(x + 2) = 323 Reorder the terms: (1 + x)(x + 2) = 323 Reorder the terms: (1 + x)(2 + x) = 323 Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x)) = 323 ((2 * 1 + x * 1) + x(2 + x)) = 323 ((2 + 1x) + x(2 + x)) = 323 (2 + 1x + (2 * x + x * x)) = 323 (2 + 1x + (2x + x2)) = 323 Combine like terms: 1x + 2x = 3x (2 + 3x + x2) = 323 Solving 2 + 3x + x2 = 323 Solving for variable 'x'. Reorder the terms: 2 + -323 + 3x + x2 = 323 + -323 Combine like terms: 2 + -323 = -321 -321 + 3x + x2 = 323 + -323 Combine like terms: 323 + -323 = 0 -321 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '321' to each side of the equation. -321 + 3x + 321 + x2 = 0 + 321 Reorder the terms: -321 + 321 + 3x + x2 = 0 + 321 Combine like terms: -321 + 321 = 0 0 + 3x + x2 = 0 + 321 3x + x2 = 0 + 321 Combine like terms: 0 + 321 = 321 3x + x2 = 321 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 = 321 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 321 + 2.25 Combine like terms: 321 + 2.25 = 323.25 2.25 + 3x + x2 = 323.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 323.25 Calculate the square root of the right side: 17.979154596 Break this problem into two subproblems by setting (x + 1.5) equal to 17.979154596 and -17.979154596.Subproblem 1
x + 1.5 = 17.979154596 Simplifying x + 1.5 = 17.979154596 Reorder the terms: 1.5 + x = 17.979154596 Solving 1.5 + x = 17.979154596 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 = 17.979154596 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 17.979154596 + -1.5 x = 17.979154596 + -1.5 Combine like terms: 17.979154596 + -1.5 = 16.479154596 x = 16.479154596 Simplifying x = 16.479154596Subproblem 2
x + 1.5 = -17.979154596 Simplifying x + 1.5 = -17.979154596 Reorder the terms: 1.5 + x = -17.979154596 Solving 1.5 + x = -17.979154596 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 = -17.979154596 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -17.979154596 + -1.5 x = -17.979154596 + -1.5 Combine like terms: -17.979154596 + -1.5 = -19.479154596 x = -19.479154596 Simplifying x = -19.479154596Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.479154596, -19.479154596}
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