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Simplifying (x + 3)(x) + (x + -8) = 55 Reorder the terms: (3 + x)(x) + (x + -8) = 55 Reorder the terms for easier multiplication: x(3 + x) + (x + -8) = 55 (3 * x + x * x) + (x + -8) = 55 (3x + x2) + (x + -8) = 55 Reorder the terms: 3x + x2 + (-8 + x) = 55 Remove parenthesis around (-8 + x) 3x + x2 + -8 + x = 55 Reorder the terms: -8 + 3x + x + x2 = 55 Combine like terms: 3x + x = 4x -8 + 4x + x2 = 55 Solving -8 + 4x + x2 = 55 Solving for variable 'x'. Reorder the terms: -8 + -55 + 4x + x2 = 55 + -55 Combine like terms: -8 + -55 = -63 -63 + 4x + x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -63 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 4x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 4x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 4x + x2 = 0 + 63 4x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 4x + x2 = 63 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 = 63 + 4 Reorder the terms: 4 + 4x + x2 = 63 + 4 Combine like terms: 63 + 4 = 67 4 + 4x + x2 = 67 Factor a perfect square on the left side: (x + 2)(x + 2) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 2) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 2 = 8.185352772 Simplifying x + 2 = 8.185352772 Reorder the terms: 2 + x = 8.185352772 Solving 2 + x = 8.185352772 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 = 8.185352772 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.185352772 + -2 x = 8.185352772 + -2 Combine like terms: 8.185352772 + -2 = 6.185352772 x = 6.185352772 Simplifying x = 6.185352772Subproblem 2
x + 2 = -8.185352772 Simplifying x + 2 = -8.185352772 Reorder the terms: 2 + x = -8.185352772 Solving 2 + x = -8.185352772 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 = -8.185352772 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.185352772 + -2 x = -8.185352772 + -2 Combine like terms: -8.185352772 + -2 = -10.185352772 x = -10.185352772 Simplifying x = -10.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.185352772, -10.185352772}
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