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Simplifying (x + 2)(x + 4) + -1 = 4(x + 2x + 4) Reorder the terms: (2 + x)(x + 4) + -1 = 4(x + 2x + 4) Reorder the terms: (2 + x)(4 + x) + -1 = 4(x + 2x + 4) Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) + -1 = 4(x + 2x + 4) ((4 * 2 + x * 2) + x(4 + x)) + -1 = 4(x + 2x + 4) ((8 + 2x) + x(4 + x)) + -1 = 4(x + 2x + 4) (8 + 2x + (4 * x + x * x)) + -1 = 4(x + 2x + 4) (8 + 2x + (4x + x2)) + -1 = 4(x + 2x + 4) Combine like terms: 2x + 4x = 6x (8 + 6x + x2) + -1 = 4(x + 2x + 4) Reorder the terms: 8 + -1 + 6x + x2 = 4(x + 2x + 4) Combine like terms: 8 + -1 = 7 7 + 6x + x2 = 4(x + 2x + 4) Reorder the terms: 7 + 6x + x2 = 4(4 + x + 2x) Combine like terms: x + 2x = 3x 7 + 6x + x2 = 4(4 + 3x) 7 + 6x + x2 = (4 * 4 + 3x * 4) 7 + 6x + x2 = (16 + 12x) Solving 7 + 6x + x2 = 16 + 12x Solving for variable 'x'. Reorder the terms: 7 + -16 + 6x + -12x + x2 = 16 + 12x + -16 + -12x Combine like terms: 7 + -16 = -9 -9 + 6x + -12x + x2 = 16 + 12x + -16 + -12x Combine like terms: 6x + -12x = -6x -9 + -6x + x2 = 16 + 12x + -16 + -12x Reorder the terms: -9 + -6x + x2 = 16 + -16 + 12x + -12x Combine like terms: 16 + -16 = 0 -9 + -6x + x2 = 0 + 12x + -12x -9 + -6x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -9 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -6x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6x + x2 = 0 + 9 -6x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6x + x2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6x + x2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6x + x2 = 18 Factor a perfect square on the left side: (x + -3)(x + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -3 = 4.242640687 Simplifying x + -3 = 4.242640687 Reorder the terms: -3 + x = 4.242640687 Solving -3 + x = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.242640687 + 3 x = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 x = 7.242640687 Simplifying x = 7.242640687Subproblem 2
x + -3 = -4.242640687 Simplifying x + -3 = -4.242640687 Reorder the terms: -3 + x = -4.242640687 Solving -3 + x = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.242640687 + 3 x = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 x = -1.242640687 Simplifying x = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.242640687, -1.242640687}
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