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Simplifying (2x + 8)(x + 6) + 3(x + -2) = 0 Reorder the terms: (8 + 2x)(x + 6) + 3(x + -2) = 0 Reorder the terms: (8 + 2x)(6 + x) + 3(x + -2) = 0 Multiply (8 + 2x) * (6 + x) (8(6 + x) + 2x * (6 + x)) + 3(x + -2) = 0 ((6 * 8 + x * 8) + 2x * (6 + x)) + 3(x + -2) = 0 ((48 + 8x) + 2x * (6 + x)) + 3(x + -2) = 0 (48 + 8x + (6 * 2x + x * 2x)) + 3(x + -2) = 0 (48 + 8x + (12x + 2x2)) + 3(x + -2) = 0 Combine like terms: 8x + 12x = 20x (48 + 20x + 2x2) + 3(x + -2) = 0 Reorder the terms: 48 + 20x + 2x2 + 3(-2 + x) = 0 48 + 20x + 2x2 + (-2 * 3 + x * 3) = 0 48 + 20x + 2x2 + (-6 + 3x) = 0 Reorder the terms: 48 + -6 + 20x + 3x + 2x2 = 0 Combine like terms: 48 + -6 = 42 42 + 20x + 3x + 2x2 = 0 Combine like terms: 20x + 3x = 23x 42 + 23x + 2x2 = 0 Solving 42 + 23x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 21 + 11.5x + x2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + 11.5x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 11.5x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 11.5x + x2 = 0 + -21 11.5x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 11.5x + x2 = -21 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = -21 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = -21 + 33.0625 Combine like terms: -21 + 33.0625 = 12.0625 33.0625 + 11.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + 5.75) equal to 3.473110997 and -3.473110997.Subproblem 1
x + 5.75 = 3.473110997 Simplifying x + 5.75 = 3.473110997 Reorder the terms: 5.75 + x = 3.473110997 Solving 5.75 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 3.473110997 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 3.473110997 + -5.75 x = 3.473110997 + -5.75 Combine like terms: 3.473110997 + -5.75 = -2.276889003 x = -2.276889003 Simplifying x = -2.276889003Subproblem 2
x + 5.75 = -3.473110997 Simplifying x + 5.75 = -3.473110997 Reorder the terms: 5.75 + x = -3.473110997 Solving 5.75 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -3.473110997 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -3.473110997 + -5.75 x = -3.473110997 + -5.75 Combine like terms: -3.473110997 + -5.75 = -9.223110997 x = -9.223110997 Simplifying x = -9.223110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.276889003, -9.223110997}
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