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Simplifying (x + 2)(x + 4) = 2 Reorder the terms: (2 + x)(x + 4) = 2 Reorder the terms: (2 + x)(4 + x) = 2 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 2 ((4 * 2 + x * 2) + x(4 + x)) = 2 ((8 + 2x) + x(4 + x)) = 2 (8 + 2x + (4 * x + x * x)) = 2 (8 + 2x + (4x + x2)) = 2 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 2 Solving 8 + 6x + x2 = 2 Solving for variable 'x'. Reorder the terms: 8 + -2 + 6x + x2 = 2 + -2 Combine like terms: 8 + -2 = 6 6 + 6x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 6 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 6x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 6x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6x + x2 = 0 + -6 6x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 6x + x2 = -6 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 = -6 + 9 Reorder the terms: 9 + 6x + x2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + 6x + x2 = 3 Factor a perfect square on the left side: (x + 3)(x + 3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 3) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 3 = 1.732050808 Simplifying x + 3 = 1.732050808 Reorder the terms: 3 + x = 1.732050808 Solving 3 + x = 1.732050808 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 = 1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.732050808 + -3 x = 1.732050808 + -3 Combine like terms: 1.732050808 + -3 = -1.267949192 x = -1.267949192 Simplifying x = -1.267949192Subproblem 2
x + 3 = -1.732050808 Simplifying x + 3 = -1.732050808 Reorder the terms: 3 + x = -1.732050808 Solving 3 + x = -1.732050808 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 = -1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.732050808 + -3 x = -1.732050808 + -3 Combine like terms: -1.732050808 + -3 = -4.732050808 x = -4.732050808 Simplifying x = -4.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.267949192, -4.732050808}
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