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Simplifying (2x + -7)(4x + -3) = 112 Reorder the terms: (-7 + 2x)(4x + -3) = 112 Reorder the terms: (-7 + 2x)(-3 + 4x) = 112 Multiply (-7 + 2x) * (-3 + 4x) (-7(-3 + 4x) + 2x * (-3 + 4x)) = 112 ((-3 * -7 + 4x * -7) + 2x * (-3 + 4x)) = 112 ((21 + -28x) + 2x * (-3 + 4x)) = 112 (21 + -28x + (-3 * 2x + 4x * 2x)) = 112 (21 + -28x + (-6x + 8x2)) = 112 Combine like terms: -28x + -6x = -34x (21 + -34x + 8x2) = 112 Solving 21 + -34x + 8x2 = 112 Solving for variable 'x'. Reorder the terms: 21 + -112 + -34x + 8x2 = 112 + -112 Combine like terms: 21 + -112 = -91 -91 + -34x + 8x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -91 + -34x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -11.375 + -4.25x + x2 = 0 Move the constant term to the right: Add '11.375' to each side of the equation. -11.375 + -4.25x + 11.375 + x2 = 0 + 11.375 Reorder the terms: -11.375 + 11.375 + -4.25x + x2 = 0 + 11.375 Combine like terms: -11.375 + 11.375 = 0.000 0.000 + -4.25x + x2 = 0 + 11.375 -4.25x + x2 = 0 + 11.375 Combine like terms: 0 + 11.375 = 11.375 -4.25x + x2 = 11.375 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 11.375 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 11.375 + 4.515625 Combine like terms: 11.375 + 4.515625 = 15.890625 4.515625 + -4.25x + x2 = 15.890625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 15.890625 Calculate the square root of the right side: 3.98630468 Break this problem into two subproblems by setting (x + -2.125) equal to 3.98630468 and -3.98630468.Subproblem 1
x + -2.125 = 3.98630468 Simplifying x + -2.125 = 3.98630468 Reorder the terms: -2.125 + x = 3.98630468 Solving -2.125 + x = 3.98630468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 3.98630468 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 3.98630468 + 2.125 x = 3.98630468 + 2.125 Combine like terms: 3.98630468 + 2.125 = 6.11130468 x = 6.11130468 Simplifying x = 6.11130468Subproblem 2
x + -2.125 = -3.98630468 Simplifying x + -2.125 = -3.98630468 Reorder the terms: -2.125 + x = -3.98630468 Solving -2.125 + x = -3.98630468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -3.98630468 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -3.98630468 + 2.125 x = -3.98630468 + 2.125 Combine like terms: -3.98630468 + 2.125 = -1.86130468 x = -1.86130468 Simplifying x = -1.86130468Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.11130468, -1.86130468}
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