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Simplifying (2x + -7)(4x + 3) = 12 Reorder the terms: (-7 + 2x)(4x + 3) = 12 Reorder the terms: (-7 + 2x)(3 + 4x) = 12 Multiply (-7 + 2x) * (3 + 4x) (-7(3 + 4x) + 2x * (3 + 4x)) = 12 ((3 * -7 + 4x * -7) + 2x * (3 + 4x)) = 12 ((-21 + -28x) + 2x * (3 + 4x)) = 12 (-21 + -28x + (3 * 2x + 4x * 2x)) = 12 (-21 + -28x + (6x + 8x2)) = 12 Combine like terms: -28x + 6x = -22x (-21 + -22x + 8x2) = 12 Solving -21 + -22x + 8x2 = 12 Solving for variable 'x'. Reorder the terms: -21 + -12 + -22x + 8x2 = 12 + -12 Combine like terms: -21 + -12 = -33 -33 + -22x + 8x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -33 + -22x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.125 + -2.75x + x2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + -2.75x + 4.125 + x2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + -2.75x + x2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + -2.75x + x2 = 0 + 4.125 -2.75x + x2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 -2.75x + x2 = 4.125 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 = 4.125 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 4.125 + 1.890625 Combine like terms: 4.125 + 1.890625 = 6.015625 1.890625 + -2.75x + x2 = 6.015625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + -1.375) equal to 2.452677109 and -2.452677109.Subproblem 1
x + -1.375 = 2.452677109 Simplifying x + -1.375 = 2.452677109 Reorder the terms: -1.375 + x = 2.452677109 Solving -1.375 + x = 2.452677109 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 = 2.452677109 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.452677109 + 1.375 x = 2.452677109 + 1.375 Combine like terms: 2.452677109 + 1.375 = 3.827677109 x = 3.827677109 Simplifying x = 3.827677109Subproblem 2
x + -1.375 = -2.452677109 Simplifying x + -1.375 = -2.452677109 Reorder the terms: -1.375 + x = -2.452677109 Solving -1.375 + x = -2.452677109 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 = -2.452677109 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.452677109 + 1.375 x = -2.452677109 + 1.375 Combine like terms: -2.452677109 + 1.375 = -1.077677109 x = -1.077677109 Simplifying x = -1.077677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.827677109, -1.077677109}
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