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Simplifying (x + 6)(2x + -4) = 939 Reorder the terms: (6 + x)(2x + -4) = 939 Reorder the terms: (6 + x)(-4 + 2x) = 939 Multiply (6 + x) * (-4 + 2x) (6(-4 + 2x) + x(-4 + 2x)) = 939 ((-4 * 6 + 2x * 6) + x(-4 + 2x)) = 939 ((-24 + 12x) + x(-4 + 2x)) = 939 (-24 + 12x + (-4 * x + 2x * x)) = 939 (-24 + 12x + (-4x + 2x2)) = 939 Combine like terms: 12x + -4x = 8x (-24 + 8x + 2x2) = 939 Solving -24 + 8x + 2x2 = 939 Solving for variable 'x'. Reorder the terms: -24 + -939 + 8x + 2x2 = 939 + -939 Combine like terms: -24 + -939 = -963 -963 + 8x + 2x2 = 939 + -939 Combine like terms: 939 + -939 = 0 -963 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -481.5 + 4x + x2 = 0 Move the constant term to the right: Add '481.5' to each side of the equation. -481.5 + 4x + 481.5 + x2 = 0 + 481.5 Reorder the terms: -481.5 + 481.5 + 4x + x2 = 0 + 481.5 Combine like terms: -481.5 + 481.5 = 0.0 0.0 + 4x + x2 = 0 + 481.5 4x + x2 = 0 + 481.5 Combine like terms: 0 + 481.5 = 481.5 4x + x2 = 481.5 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 = 481.5 + 4 Reorder the terms: 4 + 4x + x2 = 481.5 + 4 Combine like terms: 481.5 + 4 = 485.5 4 + 4x + x2 = 485.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 485.5 Calculate the square root of the right side: 22.034064537 Break this problem into two subproblems by setting (x + 2) equal to 22.034064537 and -22.034064537.Subproblem 1
x + 2 = 22.034064537 Simplifying x + 2 = 22.034064537 Reorder the terms: 2 + x = 22.034064537 Solving 2 + x = 22.034064537 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 = 22.034064537 + -2 Combine like terms: 2 + -2 = 0 0 + x = 22.034064537 + -2 x = 22.034064537 + -2 Combine like terms: 22.034064537 + -2 = 20.034064537 x = 20.034064537 Simplifying x = 20.034064537Subproblem 2
x + 2 = -22.034064537 Simplifying x + 2 = -22.034064537 Reorder the terms: 2 + x = -22.034064537 Solving 2 + x = -22.034064537 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 = -22.034064537 + -2 Combine like terms: 2 + -2 = 0 0 + x = -22.034064537 + -2 x = -22.034064537 + -2 Combine like terms: -22.034064537 + -2 = -24.034064537 x = -24.034064537 Simplifying x = -24.034064537Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.034064537, -24.034064537}
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