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Simplifying 5a2 = 31a + 28 Reorder the terms: 5a2 = 28 + 31a Solving 5a2 = 28 + 31a Solving for variable 'a'. Reorder the terms: -28 + -31a + 5a2 = 28 + 31a + -28 + -31a Reorder the terms: -28 + -31a + 5a2 = 28 + -28 + 31a + -31a Combine like terms: 28 + -28 = 0 -28 + -31a + 5a2 = 0 + 31a + -31a -28 + -31a + 5a2 = 31a + -31a Combine like terms: 31a + -31a = 0 -28 + -31a + 5a2 = 0 Factor a trinomial. (-4 + -5a)(7 + -1a) = 0Subproblem 1
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 = -0.8Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve: Simplifying 7 + -1a = 0 Solving 7 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1a = 0 + -7 -1a = 0 + -7 Combine like terms: 0 + -7 = -7 -1a = -7 Divide each side by '-1'. a = 7 Simplifying a = 7Solution
a = {-0.8, 7}
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