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Simplifying (4x + 3)(6x + -1) = 9 + -34 Reorder the terms: (3 + 4x)(6x + -1) = 9 + -34 Reorder the terms: (3 + 4x)(-1 + 6x) = 9 + -34 Multiply (3 + 4x) * (-1 + 6x) (3(-1 + 6x) + 4x * (-1 + 6x)) = 9 + -34 ((-1 * 3 + 6x * 3) + 4x * (-1 + 6x)) = 9 + -34 ((-3 + 18x) + 4x * (-1 + 6x)) = 9 + -34 (-3 + 18x + (-1 * 4x + 6x * 4x)) = 9 + -34 (-3 + 18x + (-4x + 24x2)) = 9 + -34 Combine like terms: 18x + -4x = 14x (-3 + 14x + 24x2) = 9 + -34 Combine like terms: 9 + -34 = -25 -3 + 14x + 24x2 = -25 Solving -3 + 14x + 24x2 = -25 Solving for variable 'x'. Reorder the terms: -3 + 25 + 14x + 24x2 = -25 + 25 Combine like terms: -3 + 25 = 22 22 + 14x + 24x2 = -25 + 25 Combine like terms: -25 + 25 = 0 22 + 14x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 7x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 7x + 12x2)' equal to zero and attempt to solve: Simplifying 11 + 7x + 12x2 = 0 Solving 11 + 7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.9166666667 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '-0.9166666667' to each side of the equation. 0.9166666667 + 0.5833333333x + -0.9166666667 + x2 = 0 + -0.9166666667 Reorder the terms: 0.9166666667 + -0.9166666667 + 0.5833333333x + x2 = 0 + -0.9166666667 Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000 0.0000000000 + 0.5833333333x + x2 = 0 + -0.9166666667 0.5833333333x + x2 = 0 + -0.9166666667 Combine like terms: 0 + -0.9166666667 = -0.9166666667 0.5833333333x + x2 = -0.9166666667 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = -0.9166666667 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = -0.9166666667 + 0.08506944446 Combine like terms: -0.9166666667 + 0.08506944446 = -0.83159722224 0.08506944446 + 0.5833333333x + x2 = -0.83159722224 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = -0.83159722224 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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