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Simplifying 10a2 = 3a + 4 Reorder the terms: 10a2 = 4 + 3a Solving 10a2 = 4 + 3a Solving for variable 'a'. Reorder the terms: -4 + -3a + 10a2 = 4 + 3a + -4 + -3a Reorder the terms: -4 + -3a + 10a2 = 4 + -4 + 3a + -3a Combine like terms: 4 + -4 = 0 -4 + -3a + 10a2 = 0 + 3a + -3a -4 + -3a + 10a2 = 3a + -3a Combine like terms: 3a + -3a = 0 -4 + -3a + 10a2 = 0 Factor a trinomial. (-1 + -2a)(4 + -5a) = 0Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(4 + -5a)' equal to zero and attempt to solve: Simplifying 4 + -5a = 0 Solving 4 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5a = 0 + -4 -5a = 0 + -4 Combine like terms: 0 + -4 = -4 -5a = -4 Divide each side by '-5'. a = 0.8 Simplifying a = 0.8Solution
a = {-0.5, 0.8}
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