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Simplifying (x + 2)(x + 2) = 432 Reorder the terms: (2 + x)(x + 2) = 432 Reorder the terms: (2 + x)(2 + x) = 432 Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x)) = 432 ((2 * 2 + x * 2) + x(2 + x)) = 432 ((4 + 2x) + x(2 + x)) = 432 (4 + 2x + (2 * x + x * x)) = 432 (4 + 2x + (2x + x2)) = 432 Combine like terms: 2x + 2x = 4x (4 + 4x + x2) = 432 Solving 4 + 4x + x2 = 432 Solving for variable 'x'. Reorder the terms: 4 + -432 + 4x + x2 = 432 + -432 Combine like terms: 4 + -432 = -428 -428 + 4x + x2 = 432 + -432 Combine like terms: 432 + -432 = 0 -428 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '428' to each side of the equation. -428 + 4x + 428 + x2 = 0 + 428 Reorder the terms: -428 + 428 + 4x + x2 = 0 + 428 Combine like terms: -428 + 428 = 0 0 + 4x + x2 = 0 + 428 4x + x2 = 0 + 428 Combine like terms: 0 + 428 = 428 4x + x2 = 428 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 = 428 + 4 Reorder the terms: 4 + 4x + x2 = 428 + 4 Combine like terms: 428 + 4 = 432 4 + 4x + x2 = 432 Factor a perfect square on the left side: (x + 2)(x + 2) = 432 Calculate the square root of the right side: 20.784609691 Break this problem into two subproblems by setting (x + 2) equal to 20.784609691 and -20.784609691.Subproblem 1
x + 2 = 20.784609691 Simplifying x + 2 = 20.784609691 Reorder the terms: 2 + x = 20.784609691 Solving 2 + x = 20.784609691 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 = 20.784609691 + -2 Combine like terms: 2 + -2 = 0 0 + x = 20.784609691 + -2 x = 20.784609691 + -2 Combine like terms: 20.784609691 + -2 = 18.784609691 x = 18.784609691 Simplifying x = 18.784609691Subproblem 2
x + 2 = -20.784609691 Simplifying x + 2 = -20.784609691 Reorder the terms: 2 + x = -20.784609691 Solving 2 + x = -20.784609691 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 = -20.784609691 + -2 Combine like terms: 2 + -2 = 0 0 + x = -20.784609691 + -2 x = -20.784609691 + -2 Combine like terms: -20.784609691 + -2 = -22.784609691 x = -22.784609691 Simplifying x = -22.784609691Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.784609691, -22.784609691}
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