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Simplifying -5a2(2a2 + -5a + 2) = 0 Reorder the terms: -5a2(2 + -5a + 2a2) = 0 (2 * -5a2 + -5a * -5a2 + 2a2 * -5a2) = 0 (-10a2 + 25a3 + -10a4) = 0 Solving -10a2 + 25a3 + -10a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a2'. 5a2(-2 + 5a + -2a2) = 0 Factor a trinomial. 5a2((-2 + a)(1 + -2a)) = 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 '(-2 + a)' equal to zero and attempt to solve: Simplifying -2 + a = 0 Solving -2 + a = 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 + a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + a = 0 + 2 a = 0 + 2 Combine like terms: 0 + 2 = 2 a = 2 Simplifying a = 2Subproblem 3
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {0, 2, 0.5}
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