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Simplifying 256 = (4 + x)(2 + x) Multiply (4 + x) * (2 + x) 256 = (4(2 + x) + x(2 + x)) 256 = ((2 * 4 + x * 4) + x(2 + x)) 256 = ((8 + 4x) + x(2 + x)) 256 = (8 + 4x + (2 * x + x * x)) 256 = (8 + 4x + (2x + x2)) Combine like terms: 4x + 2x = 6x 256 = (8 + 6x + x2) Solving 256 = 8 + 6x + x2 Solving for variable 'x'. Combine like terms: 256 + -8 = 248 248 + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2 Reorder the terms: 248 + -6x + -1x2 = 8 + -8 + 6x + -6x + x2 + -1x2 Combine like terms: 8 + -8 = 0 248 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 248 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 248 + -6x + -1x2 = 0 + x2 + -1x2 248 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 248 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -248 + 6x + x2 = 0 Move the constant term to the right: Add '248' to each side of the equation. -248 + 6x + 248 + x2 = 0 + 248 Reorder the terms: -248 + 248 + 6x + x2 = 0 + 248 Combine like terms: -248 + 248 = 0 0 + 6x + x2 = 0 + 248 6x + x2 = 0 + 248 Combine like terms: 0 + 248 = 248 6x + x2 = 248 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 = 248 + 9 Reorder the terms: 9 + 6x + x2 = 248 + 9 Combine like terms: 248 + 9 = 257 9 + 6x + x2 = 257 Factor a perfect square on the left side: (x + 3)(x + 3) = 257 Calculate the square root of the right side: 16.031219542 Break this problem into two subproblems by setting (x + 3) equal to 16.031219542 and -16.031219542.Subproblem 1
x + 3 = 16.031219542 Simplifying x + 3 = 16.031219542 Reorder the terms: 3 + x = 16.031219542 Solving 3 + x = 16.031219542 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 = 16.031219542 + -3 Combine like terms: 3 + -3 = 0 0 + x = 16.031219542 + -3 x = 16.031219542 + -3 Combine like terms: 16.031219542 + -3 = 13.031219542 x = 13.031219542 Simplifying x = 13.031219542Subproblem 2
x + 3 = -16.031219542 Simplifying x + 3 = -16.031219542 Reorder the terms: 3 + x = -16.031219542 Solving 3 + x = -16.031219542 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 = -16.031219542 + -3 Combine like terms: 3 + -3 = 0 0 + x = -16.031219542 + -3 x = -16.031219542 + -3 Combine like terms: -16.031219542 + -3 = -19.031219542 x = -19.031219542 Simplifying x = -19.031219542Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.031219542, -19.031219542}
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