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Simplifying 10a2 = 10 + -21a Solving 10a2 = 10 + -21a Solving for variable 'a'. Reorder the terms: -10 + 21a + 10a2 = 10 + -21a + -10 + 21a Reorder the terms: -10 + 21a + 10a2 = 10 + -10 + -21a + 21a Combine like terms: 10 + -10 = 0 -10 + 21a + 10a2 = 0 + -21a + 21a -10 + 21a + 10a2 = -21a + 21a Combine like terms: -21a + 21a = 0 -10 + 21a + 10a2 = 0 Factor a trinomial. (-5 + -2a)(2 + -5a) = 0Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve: Simplifying -5 + -2a = 0 Solving -5 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a = 0 + 5 -2a = 0 + 5 Combine like terms: 0 + 5 = 5 -2a = 5 Divide each side by '-2'. a = -2.5 Simplifying a = -2.5Subproblem 2
Set the factor '(2 + -5a)' equal to zero and attempt to solve: Simplifying 2 + -5a = 0 Solving 2 + -5a = 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 + -5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5a = 0 + -2 -5a = 0 + -2 Combine like terms: 0 + -2 = -2 -5a = -2 Divide each side by '-5'. a = 0.4 Simplifying a = 0.4Solution
a = {-2.5, 0.4}
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