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Simplifying 18a4 + -33a3 + 14a2 = 0 Reorder the terms: 14a2 + -33a3 + 18a4 = 0 Solving 14a2 + -33a3 + 18a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a2'. a2(14 + -33a + 18a2) = 0 Factor a trinomial. a2((2 + -3a)(7 + -6a)) = 0Subproblem 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 '(2 + -3a)' equal to zero and attempt to solve: Simplifying 2 + -3a = 0 Solving 2 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a = 0 + -2 -3a = 0 + -2 Combine like terms: 0 + -2 = -2 -3a = -2 Divide each side by '-3'. a = 0.6666666667 Simplifying a = 0.6666666667Subproblem 3
Set the factor '(7 + -6a)' equal to zero and attempt to solve: Simplifying 7 + -6a = 0 Solving 7 + -6a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6a = 0 + -7 -6a = 0 + -7 Combine like terms: 0 + -7 = -7 -6a = -7 Divide each side by '-6'. a = 1.166666667 Simplifying a = 1.166666667Solution
a = {0, 0.6666666667, 1.166666667}
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