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Simplifying -16 + 5x = 4x(3x + 7) Reorder the terms: -16 + 5x = 4x(7 + 3x) -16 + 5x = (7 * 4x + 3x * 4x) -16 + 5x = (28x + 12x2) Solving -16 + 5x = 28x + 12x2 Solving for variable 'x'. Combine like terms: 5x + -28x = -23x -16 + -23x + -12x2 = 28x + 12x2 + -28x + -12x2 Reorder the terms: -16 + -23x + -12x2 = 28x + -28x + 12x2 + -12x2 Combine like terms: 28x + -28x = 0 -16 + -23x + -12x2 = 0 + 12x2 + -12x2 -16 + -23x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -16 + -23x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 23x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 23x + 12x2)' equal to zero and attempt to solve: Simplifying 16 + 23x + 12x2 = 0 Solving 16 + 23x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.333333333 + 1.916666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 1.916666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 1.916666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 1.916666667x + x2 = 0 + -1.333333333 1.916666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 1.916666667x + x2 = -1.333333333 The x term is 1.916666667x. Take half its coefficient (0.9583333335). Square it (0.9184027781) and add it to both sides. Add '0.9184027781' to each side of the equation. 1.916666667x + 0.9184027781 + x2 = -1.333333333 + 0.9184027781 Reorder the terms: 0.9184027781 + 1.916666667x + x2 = -1.333333333 + 0.9184027781 Combine like terms: -1.333333333 + 0.9184027781 = -0.4149305549 0.9184027781 + 1.916666667x + x2 = -0.4149305549 Factor a perfect square on the left side: (x + 0.9583333335)(x + 0.9583333335) = -0.4149305549 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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