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Simplifying (2x + -3)(x + 5) = (5x + 9)(6 + 3x) Reorder the terms: (-3 + 2x)(x + 5) = (5x + 9)(6 + 3x) Reorder the terms: (-3 + 2x)(5 + x) = (5x + 9)(6 + 3x) Multiply (-3 + 2x) * (5 + x) (-3(5 + x) + 2x * (5 + x)) = (5x + 9)(6 + 3x) ((5 * -3 + x * -3) + 2x * (5 + x)) = (5x + 9)(6 + 3x) ((-15 + -3x) + 2x * (5 + x)) = (5x + 9)(6 + 3x) (-15 + -3x + (5 * 2x + x * 2x)) = (5x + 9)(6 + 3x) (-15 + -3x + (10x + 2x2)) = (5x + 9)(6 + 3x) Combine like terms: -3x + 10x = 7x (-15 + 7x + 2x2) = (5x + 9)(6 + 3x) Reorder the terms: -15 + 7x + 2x2 = (9 + 5x)(6 + 3x) Multiply (9 + 5x) * (6 + 3x) -15 + 7x + 2x2 = (9(6 + 3x) + 5x * (6 + 3x)) -15 + 7x + 2x2 = ((6 * 9 + 3x * 9) + 5x * (6 + 3x)) -15 + 7x + 2x2 = ((54 + 27x) + 5x * (6 + 3x)) -15 + 7x + 2x2 = (54 + 27x + (6 * 5x + 3x * 5x)) -15 + 7x + 2x2 = (54 + 27x + (30x + 15x2)) Combine like terms: 27x + 30x = 57x -15 + 7x + 2x2 = (54 + 57x + 15x2) Solving -15 + 7x + 2x2 = 54 + 57x + 15x2 Solving for variable 'x'. Reorder the terms: -15 + -54 + 7x + -57x + 2x2 + -15x2 = 54 + 57x + 15x2 + -54 + -57x + -15x2 Combine like terms: -15 + -54 = -69 -69 + 7x + -57x + 2x2 + -15x2 = 54 + 57x + 15x2 + -54 + -57x + -15x2 Combine like terms: 7x + -57x = -50x -69 + -50x + 2x2 + -15x2 = 54 + 57x + 15x2 + -54 + -57x + -15x2 Combine like terms: 2x2 + -15x2 = -13x2 -69 + -50x + -13x2 = 54 + 57x + 15x2 + -54 + -57x + -15x2 Reorder the terms: -69 + -50x + -13x2 = 54 + -54 + 57x + -57x + 15x2 + -15x2 Combine like terms: 54 + -54 = 0 -69 + -50x + -13x2 = 0 + 57x + -57x + 15x2 + -15x2 -69 + -50x + -13x2 = 57x + -57x + 15x2 + -15x2 Combine like terms: 57x + -57x = 0 -69 + -50x + -13x2 = 0 + 15x2 + -15x2 -69 + -50x + -13x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -69 + -50x + -13x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(69 + 50x + 13x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(69 + 50x + 13x2)' equal to zero and attempt to solve: Simplifying 69 + 50x + 13x2 = 0 Solving 69 + 50x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 5.307692308 + 3.846153846x + x2 = 0 Move the constant term to the right: Add '-5.307692308' to each side of the equation. 5.307692308 + 3.846153846x + -5.307692308 + x2 = 0 + -5.307692308 Reorder the terms: 5.307692308 + -5.307692308 + 3.846153846x + x2 = 0 + -5.307692308 Combine like terms: 5.307692308 + -5.307692308 = 0.000000000 0.000000000 + 3.846153846x + x2 = 0 + -5.307692308 3.846153846x + x2 = 0 + -5.307692308 Combine like terms: 0 + -5.307692308 = -5.307692308 3.846153846x + x2 = -5.307692308 The x term is 3.846153846x. Take half its coefficient (1.923076923). Square it (3.698224852) and add it to both sides. Add '3.698224852' to each side of the equation. 3.846153846x + 3.698224852 + x2 = -5.307692308 + 3.698224852 Reorder the terms: 3.698224852 + 3.846153846x + x2 = -5.307692308 + 3.698224852 Combine like terms: -5.307692308 + 3.698224852 = -1.609467456 3.698224852 + 3.846153846x + x2 = -1.609467456 Factor a perfect square on the left side: (x + 1.923076923)(x + 1.923076923) = -1.609467456 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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