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Simplifying (x + 2)(x + 4) = 340 Reorder the terms: (2 + x)(x + 4) = 340 Reorder the terms: (2 + x)(4 + x) = 340 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 340 ((4 * 2 + x * 2) + x(4 + x)) = 340 ((8 + 2x) + x(4 + x)) = 340 (8 + 2x + (4 * x + x * x)) = 340 (8 + 2x + (4x + x2)) = 340 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 340 Solving 8 + 6x + x2 = 340 Solving for variable 'x'. Reorder the terms: 8 + -340 + 6x + x2 = 340 + -340 Combine like terms: 8 + -340 = -332 -332 + 6x + x2 = 340 + -340 Combine like terms: 340 + -340 = 0 -332 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '332' to each side of the equation. -332 + 6x + 332 + x2 = 0 + 332 Reorder the terms: -332 + 332 + 6x + x2 = 0 + 332 Combine like terms: -332 + 332 = 0 0 + 6x + x2 = 0 + 332 6x + x2 = 0 + 332 Combine like terms: 0 + 332 = 332 6x + x2 = 332 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 = 332 + 9 Reorder the terms: 9 + 6x + x2 = 332 + 9 Combine like terms: 332 + 9 = 341 9 + 6x + x2 = 341 Factor a perfect square on the left side: (x + 3)(x + 3) = 341 Calculate the square root of the right side: 18.466185313 Break this problem into two subproblems by setting (x + 3) equal to 18.466185313 and -18.466185313.Subproblem 1
x + 3 = 18.466185313 Simplifying x + 3 = 18.466185313 Reorder the terms: 3 + x = 18.466185313 Solving 3 + x = 18.466185313 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 = 18.466185313 + -3 Combine like terms: 3 + -3 = 0 0 + x = 18.466185313 + -3 x = 18.466185313 + -3 Combine like terms: 18.466185313 + -3 = 15.466185313 x = 15.466185313 Simplifying x = 15.466185313Subproblem 2
x + 3 = -18.466185313 Simplifying x + 3 = -18.466185313 Reorder the terms: 3 + x = -18.466185313 Solving 3 + x = -18.466185313 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 = -18.466185313 + -3 Combine like terms: 3 + -3 = 0 0 + x = -18.466185313 + -3 x = -18.466185313 + -3 Combine like terms: -18.466185313 + -3 = -21.466185313 x = -21.466185313 Simplifying x = -21.466185313Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.466185313, -21.466185313}
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