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Simplifying 4a2 = 10 + -3a Solving 4a2 = 10 + -3a Solving for variable 'a'. Reorder the terms: -10 + 3a + 4a2 = 10 + -3a + -10 + 3a Reorder the terms: -10 + 3a + 4a2 = 10 + -10 + -3a + 3a Combine like terms: 10 + -10 = 0 -10 + 3a + 4a2 = 0 + -3a + 3a -10 + 3a + 4a2 = -3a + 3a Combine like terms: -3a + 3a = 0 -10 + 3a + 4a2 = 0 Factor a trinomial. (-2 + -1a)(5 + -4a) = 0Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 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 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2Subproblem 2
Set the factor '(5 + -4a)' equal to zero and attempt to solve: Simplifying 5 + -4a = 0 Solving 5 + -4a = 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 + -4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4a = 0 + -5 -4a = 0 + -5 Combine like terms: 0 + -5 = -5 -4a = -5 Divide each side by '-4'. a = 1.25 Simplifying a = 1.25Solution
a = {-2, 1.25}
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