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Simplifying (3x + 8)(x + 8) = 832 Reorder the terms: (8 + 3x)(x + 8) = 832 Reorder the terms: (8 + 3x)(8 + x) = 832 Multiply (8 + 3x) * (8 + x) (8(8 + x) + 3x * (8 + x)) = 832 ((8 * 8 + x * 8) + 3x * (8 + x)) = 832 ((64 + 8x) + 3x * (8 + x)) = 832 (64 + 8x + (8 * 3x + x * 3x)) = 832 (64 + 8x + (24x + 3x2)) = 832 Combine like terms: 8x + 24x = 32x (64 + 32x + 3x2) = 832 Solving 64 + 32x + 3x2 = 832 Solving for variable 'x'. Reorder the terms: 64 + -832 + 32x + 3x2 = 832 + -832 Combine like terms: 64 + -832 = -768 -768 + 32x + 3x2 = 832 + -832 Combine like terms: 832 + -832 = 0 -768 + 32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -256 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + 10.66666667x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 10.66666667x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 10.66666667x + x2 = 0 + 256 10.66666667x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 10.66666667x + x2 = 256 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = 256 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = 256 + 28.44444446 Combine like terms: 256 + 28.44444446 = 284.44444446 28.44444446 + 10.66666667x + x2 = 284.44444446 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 284.44444446 Calculate the square root of the right side: 16.865480855 Break this problem into two subproblems by setting (x + 5.333333335) equal to 16.865480855 and -16.865480855.Subproblem 1
x + 5.333333335 = 16.865480855 Simplifying x + 5.333333335 = 16.865480855 Reorder the terms: 5.333333335 + x = 16.865480855 Solving 5.333333335 + x = 16.865480855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 16.865480855 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 16.865480855 + -5.333333335 x = 16.865480855 + -5.333333335 Combine like terms: 16.865480855 + -5.333333335 = 11.53214752 x = 11.53214752 Simplifying x = 11.53214752Subproblem 2
x + 5.333333335 = -16.865480855 Simplifying x + 5.333333335 = -16.865480855 Reorder the terms: 5.333333335 + x = -16.865480855 Solving 5.333333335 + x = -16.865480855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -16.865480855 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -16.865480855 + -5.333333335 x = -16.865480855 + -5.333333335 Combine like terms: -16.865480855 + -5.333333335 = -22.19881419 x = -22.19881419 Simplifying x = -22.19881419Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.53214752, -22.19881419}
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