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Simplifying (4x + -5)(3x + 6) = 142 Reorder the terms: (-5 + 4x)(3x + 6) = 142 Reorder the terms: (-5 + 4x)(6 + 3x) = 142 Multiply (-5 + 4x) * (6 + 3x) (-5(6 + 3x) + 4x * (6 + 3x)) = 142 ((6 * -5 + 3x * -5) + 4x * (6 + 3x)) = 142 ((-30 + -15x) + 4x * (6 + 3x)) = 142 (-30 + -15x + (6 * 4x + 3x * 4x)) = 142 (-30 + -15x + (24x + 12x2)) = 142 Combine like terms: -15x + 24x = 9x (-30 + 9x + 12x2) = 142 Solving -30 + 9x + 12x2 = 142 Solving for variable 'x'. Reorder the terms: -30 + -142 + 9x + 12x2 = 142 + -142 Combine like terms: -30 + -142 = -172 -172 + 9x + 12x2 = 142 + -142 Combine like terms: 142 + -142 = 0 -172 + 9x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -14.33333333 + 0.75x + x2 = 0 Move the constant term to the right: Add '14.33333333' to each side of the equation. -14.33333333 + 0.75x + 14.33333333 + x2 = 0 + 14.33333333 Reorder the terms: -14.33333333 + 14.33333333 + 0.75x + x2 = 0 + 14.33333333 Combine like terms: -14.33333333 + 14.33333333 = 0.00000000 0.00000000 + 0.75x + x2 = 0 + 14.33333333 0.75x + x2 = 0 + 14.33333333 Combine like terms: 0 + 14.33333333 = 14.33333333 0.75x + x2 = 14.33333333 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 14.33333333 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 14.33333333 + 0.140625 Combine like terms: 14.33333333 + 0.140625 = 14.47395833 0.140625 + 0.75x + x2 = 14.47395833 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 14.47395833 Calculate the square root of the right side: 3.804465577 Break this problem into two subproblems by setting (x + 0.375) equal to 3.804465577 and -3.804465577.Subproblem 1
x + 0.375 = 3.804465577 Simplifying x + 0.375 = 3.804465577 Reorder the terms: 0.375 + x = 3.804465577 Solving 0.375 + x = 3.804465577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 3.804465577 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 3.804465577 + -0.375 x = 3.804465577 + -0.375 Combine like terms: 3.804465577 + -0.375 = 3.429465577 x = 3.429465577 Simplifying x = 3.429465577Subproblem 2
x + 0.375 = -3.804465577 Simplifying x + 0.375 = -3.804465577 Reorder the terms: 0.375 + x = -3.804465577 Solving 0.375 + x = -3.804465577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -3.804465577 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -3.804465577 + -0.375 x = -3.804465577 + -0.375 Combine like terms: -3.804465577 + -0.375 = -4.179465577 x = -4.179465577 Simplifying x = -4.179465577Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.429465577, -4.179465577}
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