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Simplifying 3a2 + 14a + 3a3 = 0 Reorder the terms: 14a + 3a2 + 3a3 = 0 Solving 14a + 3a2 + 3a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(14 + 3a + 3a2) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(14 + 3a + 3a2)' equal to zero and attempt to solve: Simplifying 14 + 3a + 3a2 = 0 Solving 14 + 3a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.666666667 + a + a2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + a + -4.666666667 + a2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + a + a2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + a + a2 = 0 + -4.666666667 a + a2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 a + a2 = -4.666666667 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = -4.666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = -4.666666667 + 0.25 Combine like terms: -4.666666667 + 0.25 = -4.416666667 1.25 + a2 = -4.416666667 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -4.416666667 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.Solution
a = {0}
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