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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 = -22x (-21 + -22x + 8x2) = 112 Solving -21 + -22x + 8x2 = 112 Solving for variable 'x'. Reorder the terms: -21 + -112 + -22x + 8x2 = 112 + -112 Combine like terms: -21 + -112 = -133 -133 + -22x + 8x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -133 + -22x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -16.625 + -2.75x + x2 = 0 Move the constant term to the right: Add '16.625' to each side of the equation. -16.625 + -2.75x + 16.625 + x2 = 0 + 16.625 Reorder the terms: -16.625 + 16.625 + -2.75x + x2 = 0 + 16.625 Combine like terms: -16.625 + 16.625 = 0.000 0.000 + -2.75x + x2 = 0 + 16.625 -2.75x + x2 = 0 + 16.625 Combine like terms: 0 + 16.625 = 16.625 -2.75x + x2 = 16.625 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 = 16.625 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 16.625 + 1.890625 Combine like terms: 16.625 + 1.890625 = 18.515625 1.890625 + -2.75x + x2 = 18.515625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 18.515625 Calculate the square root of the right side: 4.30297862 Break this problem into two subproblems by setting (x + -1.375) equal to 4.30297862 and -4.30297862.Subproblem 1
x + -1.375 = 4.30297862 Simplifying x + -1.375 = 4.30297862 Reorder the terms: -1.375 + x = 4.30297862 Solving -1.375 + x = 4.30297862 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 = 4.30297862 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 4.30297862 + 1.375 x = 4.30297862 + 1.375 Combine like terms: 4.30297862 + 1.375 = 5.67797862 x = 5.67797862 Simplifying x = 5.67797862Subproblem 2
x + -1.375 = -4.30297862 Simplifying x + -1.375 = -4.30297862 Reorder the terms: -1.375 + x = -4.30297862 Solving -1.375 + x = -4.30297862 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 = -4.30297862 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -4.30297862 + 1.375 x = -4.30297862 + 1.375 Combine like terms: -4.30297862 + 1.375 = -2.92797862 x = -2.92797862 Simplifying x = -2.92797862Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.67797862, -2.92797862}
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