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Simplifying (x + 2)(x + 4) = 432 Reorder the terms: (2 + x)(x + 4) = 432 Reorder the terms: (2 + x)(4 + x) = 432 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 432 ((4 * 2 + x * 2) + x(4 + x)) = 432 ((8 + 2x) + x(4 + x)) = 432 (8 + 2x + (4 * x + x * x)) = 432 (8 + 2x + (4x + x2)) = 432 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 432 Solving 8 + 6x + x2 = 432 Solving for variable 'x'. Reorder the terms: 8 + -432 + 6x + x2 = 432 + -432 Combine like terms: 8 + -432 = -424 -424 + 6x + x2 = 432 + -432 Combine like terms: 432 + -432 = 0 -424 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '424' to each side of the equation. -424 + 6x + 424 + x2 = 0 + 424 Reorder the terms: -424 + 424 + 6x + x2 = 0 + 424 Combine like terms: -424 + 424 = 0 0 + 6x + x2 = 0 + 424 6x + x2 = 0 + 424 Combine like terms: 0 + 424 = 424 6x + x2 = 424 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 = 424 + 9 Reorder the terms: 9 + 6x + x2 = 424 + 9 Combine like terms: 424 + 9 = 433 9 + 6x + x2 = 433 Factor a perfect square on the left side: (x + 3)(x + 3) = 433 Calculate the square root of the right side: 20.808652047 Break this problem into two subproblems by setting (x + 3) equal to 20.808652047 and -20.808652047.Subproblem 1
x + 3 = 20.808652047 Simplifying x + 3 = 20.808652047 Reorder the terms: 3 + x = 20.808652047 Solving 3 + x = 20.808652047 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 = 20.808652047 + -3 Combine like terms: 3 + -3 = 0 0 + x = 20.808652047 + -3 x = 20.808652047 + -3 Combine like terms: 20.808652047 + -3 = 17.808652047 x = 17.808652047 Simplifying x = 17.808652047Subproblem 2
x + 3 = -20.808652047 Simplifying x + 3 = -20.808652047 Reorder the terms: 3 + x = -20.808652047 Solving 3 + x = -20.808652047 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 = -20.808652047 + -3 Combine like terms: 3 + -3 = 0 0 + x = -20.808652047 + -3 x = -20.808652047 + -3 Combine like terms: -20.808652047 + -3 = -23.808652047 x = -23.808652047 Simplifying x = -23.808652047Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.808652047, -23.808652047}
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