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Simplifying 6x2 + 16x + 24 = 0 Reorder the terms: 24 + 16x + 6x2 = 0 Solving 24 + 16x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 8x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 12 + 8x + 3x2 = 0 Solving 12 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2.666666667x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 2.666666667x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2.666666667x + x2 = 0 + -4 2.666666667x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 2.666666667x + x2 = -4 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -4 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -4 + 1.777777780 Combine like terms: -4 + 1.777777780 = -2.22222222 1.777777780 + 2.666666667x + x2 = -2.22222222 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -2.22222222 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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