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Simplifying (4x + -7)(3x + 8) = 1 Reorder the terms: (-7 + 4x)(3x + 8) = 1 Reorder the terms: (-7 + 4x)(8 + 3x) = 1 Multiply (-7 + 4x) * (8 + 3x) (-7(8 + 3x) + 4x * (8 + 3x)) = 1 ((8 * -7 + 3x * -7) + 4x * (8 + 3x)) = 1 ((-56 + -21x) + 4x * (8 + 3x)) = 1 (-56 + -21x + (8 * 4x + 3x * 4x)) = 1 (-56 + -21x + (32x + 12x2)) = 1 Combine like terms: -21x + 32x = 11x (-56 + 11x + 12x2) = 1 Solving -56 + 11x + 12x2 = 1 Solving for variable 'x'. Reorder the terms: -56 + -1 + 11x + 12x2 = 1 + -1 Combine like terms: -56 + -1 = -57 -57 + 11x + 12x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -57 + 11x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4.75 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 0.9166666667x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 0.9166666667x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 0.9166666667x + x2 = 0 + 4.75 0.9166666667x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 0.9166666667x + x2 = 4.75 The x term is 0.9166666667x. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667x + 0.2100694445 + x2 = 4.75 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 4.75 + 0.2100694445 Combine like terms: 4.75 + 0.2100694445 = 4.9600694445 0.2100694445 + 0.9166666667x + x2 = 4.9600694445 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 4.9600694445 Calculate the square root of the right side: 2.227121336 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 2.227121336 and -2.227121336.Subproblem 1
x + 0.4583333334 = 2.227121336 Simplifying x + 0.4583333334 = 2.227121336 Reorder the terms: 0.4583333334 + x = 2.227121336 Solving 0.4583333334 + x = 2.227121336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 2.227121336 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 2.227121336 + -0.4583333334 x = 2.227121336 + -0.4583333334 Combine like terms: 2.227121336 + -0.4583333334 = 1.7687880026 x = 1.7687880026 Simplifying x = 1.7687880026Subproblem 2
x + 0.4583333334 = -2.227121336 Simplifying x + 0.4583333334 = -2.227121336 Reorder the terms: 0.4583333334 + x = -2.227121336 Solving 0.4583333334 + x = -2.227121336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -2.227121336 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -2.227121336 + -0.4583333334 x = -2.227121336 + -0.4583333334 Combine like terms: -2.227121336 + -0.4583333334 = -2.6854546694 x = -2.6854546694 Simplifying x = -2.6854546694Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7687880026, -2.6854546694}
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