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Simplifying (4x + -14)(8x + 6) = 128 Reorder the terms: (-14 + 4x)(8x + 6) = 128 Reorder the terms: (-14 + 4x)(6 + 8x) = 128 Multiply (-14 + 4x) * (6 + 8x) (-14(6 + 8x) + 4x * (6 + 8x)) = 128 ((6 * -14 + 8x * -14) + 4x * (6 + 8x)) = 128 ((-84 + -112x) + 4x * (6 + 8x)) = 128 (-84 + -112x + (6 * 4x + 8x * 4x)) = 128 (-84 + -112x + (24x + 32x2)) = 128 Combine like terms: -112x + 24x = -88x (-84 + -88x + 32x2) = 128 Solving -84 + -88x + 32x2 = 128 Solving for variable 'x'. Reorder the terms: -84 + -128 + -88x + 32x2 = 128 + -128 Combine like terms: -84 + -128 = -212 -212 + -88x + 32x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -212 + -88x + 32x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-53 + -22x + 8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-53 + -22x + 8x2)' equal to zero and attempt to solve: Simplifying -53 + -22x + 8x2 = 0 Solving -53 + -22x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.625 + -2.75x + x2 = 0 Move the constant term to the right: Add '6.625' to each side of the equation. -6.625 + -2.75x + 6.625 + x2 = 0 + 6.625 Reorder the terms: -6.625 + 6.625 + -2.75x + x2 = 0 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + -2.75x + x2 = 0 + 6.625 -2.75x + x2 = 0 + 6.625 Combine like terms: 0 + 6.625 = 6.625 -2.75x + x2 = 6.625 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 6.625 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 6.625 + 1.890625 Combine like terms: 6.625 + 1.890625 = 8.515625 1.890625 + -2.75x + x2 = 8.515625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 8.515625 Calculate the square root of the right side: 2.918154382 Break this problem into two subproblems by setting (x + -1.375) equal to 2.918154382 and -2.918154382.Subproblem 1
x + -1.375 = 2.918154382 Simplifying x + -1.375 = 2.918154382 Reorder the terms: -1.375 + x = 2.918154382 Solving -1.375 + x = 2.918154382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.918154382 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.918154382 + 1.375 x = 2.918154382 + 1.375 Combine like terms: 2.918154382 + 1.375 = 4.293154382 x = 4.293154382 Simplifying x = 4.293154382Subproblem 2
x + -1.375 = -2.918154382 Simplifying x + -1.375 = -2.918154382 Reorder the terms: -1.375 + x = -2.918154382 Solving -1.375 + x = -2.918154382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.918154382 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.918154382 + 1.375 x = -2.918154382 + 1.375 Combine like terms: -2.918154382 + 1.375 = -1.543154382 x = -1.543154382 Simplifying x = -1.543154382Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.293154382, -1.543154382}Solution
x = {4.293154382, -1.543154382}
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