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Simplifying (x + -2)(x + 4) = 6 Reorder the terms: (-2 + x)(x + 4) = 6 Reorder the terms: (-2 + x)(4 + x) = 6 Multiply (-2 + x) * (4 + x) (-2(4 + x) + x(4 + x)) = 6 ((4 * -2 + x * -2) + x(4 + x)) = 6 ((-8 + -2x) + x(4 + x)) = 6 (-8 + -2x + (4 * x + x * x)) = 6 (-8 + -2x + (4x + x2)) = 6 Combine like terms: -2x + 4x = 2x (-8 + 2x + x2) = 6 Solving -8 + 2x + x2 = 6 Solving for variable 'x'. Reorder the terms: -8 + -6 + 2x + x2 = 6 + -6 Combine like terms: -8 + -6 = -14 -14 + 2x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -14 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 2x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 2x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2x + x2 = 0 + 14 2x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 2x + x2 = 14 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 14 + 1 Reorder the terms: 1 + 2x + x2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + 2x + x2 = 15 Factor a perfect square on the left side: (x + 1)(x + 1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 1) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 1 = 3.872983346 Simplifying x + 1 = 3.872983346 Reorder the terms: 1 + x = 3.872983346 Solving 1 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.872983346 + -1 x = 3.872983346 + -1 Combine like terms: 3.872983346 + -1 = 2.872983346 x = 2.872983346 Simplifying x = 2.872983346Subproblem 2
x + 1 = -3.872983346 Simplifying x + 1 = -3.872983346 Reorder the terms: 1 + x = -3.872983346 Solving 1 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.872983346 + -1 x = -3.872983346 + -1 Combine like terms: -3.872983346 + -1 = -4.872983346 x = -4.872983346 Simplifying x = -4.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.872983346, -4.872983346}
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