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Simplifying 0 = 3x2 + 16x + 24 Reorder the terms: 0 = 24 + 16x + 3x2 Solving 0 = 24 + 16x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + -16x + -3x2 = 24 + 16x + 3x2 + -24 + -16x + -3x2 Reorder the terms: -24 + -16x + -3x2 = 24 + -24 + 16x + -16x + 3x2 + -3x2 Combine like terms: 24 + -24 = 0 -24 + -16x + -3x2 = 0 + 16x + -16x + 3x2 + -3x2 -24 + -16x + -3x2 = 16x + -16x + 3x2 + -3x2 Combine like terms: 16x + -16x = 0 -24 + -16x + -3x2 = 0 + 3x2 + -3x2 -24 + -16x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -24 + -16x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 16x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 16x + 3x2)' equal to zero and attempt to solve: Simplifying 24 + 16x + 3x2 = 0 Solving 24 + 16x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 5.333333333x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 5.333333333x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5.333333333x + x2 = 0 + -8 5.333333333x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 5.333333333x + x2 = -8 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = -8 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = -8 + 7.111111113 Combine like terms: -8 + 7.111111113 = -0.888888887 7.111111113 + 5.333333333x + x2 = -0.888888887 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = -0.888888887 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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