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Simplifying 4x + -5 + 4x + 3 = 3(4x + 3)(4x + 5) Reorder the terms: -5 + 3 + 4x + 4x = 3(4x + 3)(4x + 5) Combine like terms: -5 + 3 = -2 -2 + 4x + 4x = 3(4x + 3)(4x + 5) Combine like terms: 4x + 4x = 8x -2 + 8x = 3(4x + 3)(4x + 5) Reorder the terms: -2 + 8x = 3(3 + 4x)(4x + 5) Reorder the terms: -2 + 8x = 3(3 + 4x)(5 + 4x) Multiply (3 + 4x) * (5 + 4x) -2 + 8x = 3(3(5 + 4x) + 4x * (5 + 4x)) -2 + 8x = 3((5 * 3 + 4x * 3) + 4x * (5 + 4x)) -2 + 8x = 3((15 + 12x) + 4x * (5 + 4x)) -2 + 8x = 3(15 + 12x + (5 * 4x + 4x * 4x)) -2 + 8x = 3(15 + 12x + (20x + 16x2)) Combine like terms: 12x + 20x = 32x -2 + 8x = 3(15 + 32x + 16x2) -2 + 8x = (15 * 3 + 32x * 3 + 16x2 * 3) -2 + 8x = (45 + 96x + 48x2) Solving -2 + 8x = 45 + 96x + 48x2 Solving for variable 'x'. Reorder the terms: -2 + -45 + 8x + -96x + -48x2 = 45 + 96x + 48x2 + -45 + -96x + -48x2 Combine like terms: -2 + -45 = -47 -47 + 8x + -96x + -48x2 = 45 + 96x + 48x2 + -45 + -96x + -48x2 Combine like terms: 8x + -96x = -88x -47 + -88x + -48x2 = 45 + 96x + 48x2 + -45 + -96x + -48x2 Reorder the terms: -47 + -88x + -48x2 = 45 + -45 + 96x + -96x + 48x2 + -48x2 Combine like terms: 45 + -45 = 0 -47 + -88x + -48x2 = 0 + 96x + -96x + 48x2 + -48x2 -47 + -88x + -48x2 = 96x + -96x + 48x2 + -48x2 Combine like terms: 96x + -96x = 0 -47 + -88x + -48x2 = 0 + 48x2 + -48x2 -47 + -88x + -48x2 = 48x2 + -48x2 Combine like terms: 48x2 + -48x2 = 0 -47 + -88x + -48x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(47 + 88x + 48x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(47 + 88x + 48x2)' equal to zero and attempt to solve: Simplifying 47 + 88x + 48x2 = 0 Solving 47 + 88x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. 0.9791666667 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '-0.9791666667' to each side of the equation. 0.9791666667 + 1.833333333x + -0.9791666667 + x2 = 0 + -0.9791666667 Reorder the terms: 0.9791666667 + -0.9791666667 + 1.833333333x + x2 = 0 + -0.9791666667 Combine like terms: 0.9791666667 + -0.9791666667 = 0.0000000000 0.0000000000 + 1.833333333x + x2 = 0 + -0.9791666667 1.833333333x + x2 = 0 + -0.9791666667 Combine like terms: 0 + -0.9791666667 = -0.9791666667 1.833333333x + x2 = -0.9791666667 The x term is 1.833333333x. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333x + 0.8402777775 + x2 = -0.9791666667 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = -0.9791666667 + 0.8402777775 Combine like terms: -0.9791666667 + 0.8402777775 = -0.1388888892 0.8402777775 + 1.833333333x + x2 = -0.1388888892 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = -0.1388888892 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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