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Simplifying x + (x + 1)(x + 2) = 46 Reorder the terms: x + (1 + x)(x + 2) = 46 Reorder the terms: x + (1 + x)(2 + x) = 46 Multiply (1 + x) * (2 + x) x + (1(2 + x) + x(2 + x)) = 46 x + ((2 * 1 + x * 1) + x(2 + x)) = 46 x + ((2 + 1x) + x(2 + x)) = 46 x + (2 + 1x + (2 * x + x * x)) = 46 x + (2 + 1x + (2x + x2)) = 46 Combine like terms: 1x + 2x = 3x x + (2 + 3x + x2) = 46 Reorder the terms: 2 + x + 3x + x2 = 46 Combine like terms: x + 3x = 4x 2 + 4x + x2 = 46 Solving 2 + 4x + x2 = 46 Solving for variable 'x'. Reorder the terms: 2 + -46 + 4x + x2 = 46 + -46 Combine like terms: 2 + -46 = -44 -44 + 4x + x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -44 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 4x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 4x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 4x + x2 = 0 + 44 4x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 4x + x2 = 44 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 44 + 4 Reorder the terms: 4 + 4x + x2 = 44 + 4 Combine like terms: 44 + 4 = 48 4 + 4x + x2 = 48 Factor a perfect square on the left side: (x + 2)(x + 2) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 2) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 2 = 6.92820323 Simplifying x + 2 = 6.92820323 Reorder the terms: 2 + x = 6.92820323 Solving 2 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.92820323 + -2 x = 6.92820323 + -2 Combine like terms: 6.92820323 + -2 = 4.92820323 x = 4.92820323 Simplifying x = 4.92820323Subproblem 2
x + 2 = -6.92820323 Simplifying x + 2 = -6.92820323 Reorder the terms: 2 + x = -6.92820323 Solving 2 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.92820323 + -2 x = -6.92820323 + -2 Combine like terms: -6.92820323 + -2 = -8.92820323 x = -8.92820323 Simplifying x = -8.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.92820323, -8.92820323}
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