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Simplifying 0 = 10a2 + -5a Reorder the terms: 0 = -5a + 10a2 Solving 0 = -5a + 10a2 Solving for variable 'a'. Remove the zero: 5a + -10a2 = -5a + 10a2 + 5a + -10a2 Reorder the terms: 5a + -10a2 = -5a + 5a + 10a2 + -10a2 Combine like terms: -5a + 5a = 0 5a + -10a2 = 0 + 10a2 + -10a2 5a + -10a2 = 10a2 + -10a2 Combine like terms: 10a2 + -10a2 = 0 5a + -10a2 = 0 Factor out the Greatest Common Factor (GCF), '5a'. 5a(1 + -2a) = 0 Ignore the factor 5.Subproblem 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 '(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, 0.5}
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