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Simplifying (3x + 4)(6x + 7) + -5 = (6x + -7)(2x + 5) Reorder the terms: (4 + 3x)(6x + 7) + -5 = (6x + -7)(2x + 5) Reorder the terms: (4 + 3x)(7 + 6x) + -5 = (6x + -7)(2x + 5) Multiply (4 + 3x) * (7 + 6x) (4(7 + 6x) + 3x * (7 + 6x)) + -5 = (6x + -7)(2x + 5) ((7 * 4 + 6x * 4) + 3x * (7 + 6x)) + -5 = (6x + -7)(2x + 5) ((28 + 24x) + 3x * (7 + 6x)) + -5 = (6x + -7)(2x + 5) (28 + 24x + (7 * 3x + 6x * 3x)) + -5 = (6x + -7)(2x + 5) (28 + 24x + (21x + 18x2)) + -5 = (6x + -7)(2x + 5) Combine like terms: 24x + 21x = 45x (28 + 45x + 18x2) + -5 = (6x + -7)(2x + 5) Reorder the terms: 28 + -5 + 45x + 18x2 = (6x + -7)(2x + 5) Combine like terms: 28 + -5 = 23 23 + 45x + 18x2 = (6x + -7)(2x + 5) Reorder the terms: 23 + 45x + 18x2 = (-7 + 6x)(2x + 5) Reorder the terms: 23 + 45x + 18x2 = (-7 + 6x)(5 + 2x) Multiply (-7 + 6x) * (5 + 2x) 23 + 45x + 18x2 = (-7(5 + 2x) + 6x * (5 + 2x)) 23 + 45x + 18x2 = ((5 * -7 + 2x * -7) + 6x * (5 + 2x)) 23 + 45x + 18x2 = ((-35 + -14x) + 6x * (5 + 2x)) 23 + 45x + 18x2 = (-35 + -14x + (5 * 6x + 2x * 6x)) 23 + 45x + 18x2 = (-35 + -14x + (30x + 12x2)) Combine like terms: -14x + 30x = 16x 23 + 45x + 18x2 = (-35 + 16x + 12x2) Solving 23 + 45x + 18x2 = -35 + 16x + 12x2 Solving for variable 'x'. Reorder the terms: 23 + 35 + 45x + -16x + 18x2 + -12x2 = -35 + 16x + 12x2 + 35 + -16x + -12x2 Combine like terms: 23 + 35 = 58 58 + 45x + -16x + 18x2 + -12x2 = -35 + 16x + 12x2 + 35 + -16x + -12x2 Combine like terms: 45x + -16x = 29x 58 + 29x + 18x2 + -12x2 = -35 + 16x + 12x2 + 35 + -16x + -12x2 Combine like terms: 18x2 + -12x2 = 6x2 58 + 29x + 6x2 = -35 + 16x + 12x2 + 35 + -16x + -12x2 Reorder the terms: 58 + 29x + 6x2 = -35 + 35 + 16x + -16x + 12x2 + -12x2 Combine like terms: -35 + 35 = 0 58 + 29x + 6x2 = 0 + 16x + -16x + 12x2 + -12x2 58 + 29x + 6x2 = 16x + -16x + 12x2 + -12x2 Combine like terms: 16x + -16x = 0 58 + 29x + 6x2 = 0 + 12x2 + -12x2 58 + 29x + 6x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 58 + 29x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 9.666666667 + 4.833333333x + x2 = 0 Move the constant term to the right: Add '-9.666666667' to each side of the equation. 9.666666667 + 4.833333333x + -9.666666667 + x2 = 0 + -9.666666667 Reorder the terms: 9.666666667 + -9.666666667 + 4.833333333x + x2 = 0 + -9.666666667 Combine like terms: 9.666666667 + -9.666666667 = 0.000000000 0.000000000 + 4.833333333x + x2 = 0 + -9.666666667 4.833333333x + x2 = 0 + -9.666666667 Combine like terms: 0 + -9.666666667 = -9.666666667 4.833333333x + x2 = -9.666666667 The x term is 4.833333333x. Take half its coefficient (2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. 4.833333333x + 5.840277779 + x2 = -9.666666667 + 5.840277779 Reorder the terms: 5.840277779 + 4.833333333x + x2 = -9.666666667 + 5.840277779 Combine like terms: -9.666666667 + 5.840277779 = -3.826388888 5.840277779 + 4.833333333x + x2 = -3.826388888 Factor a perfect square on the left side: (x + 2.416666667)(x + 2.416666667) = -3.826388888 Can't calculate square root of the right side. The solution to this equation could not be determined.
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