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Simplifying 5a2(3a2 + a + 1) = 0 Reorder the terms: 5a2(1 + a + 3a2) = 0 (1 * 5a2 + a * 5a2 + 3a2 * 5a2) = 0 (5a2 + 5a3 + 15a4) = 0 Solving 5a2 + 5a3 + 15a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a2'. 5a2(1 + a + 3a2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(1 + a + 3a2)' equal to zero and attempt to solve: Simplifying 1 + a + 3a2 = 0 Solving 1 + a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 0.3333333333a + a2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.3333333333a + -0.3333333333 + a2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.3333333333a + a2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.3333333333a + a2 = 0 + -0.3333333333 0.3333333333a + a2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.3333333333a + a2 = -0.3333333333 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. 0.3333333333a + 0.25 + a2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333a + a2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + 0.3333333333a + a2 = -0.0833333333 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -0.0833333333 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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