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Simplifying 4a2 = 7a + 92 Reorder the terms: 4a2 = 92 + 7a Solving 4a2 = 92 + 7a Solving for variable 'a'. Reorder the terms: -92 + -7a + 4a2 = 92 + 7a + -92 + -7a Reorder the terms: -92 + -7a + 4a2 = 92 + -92 + 7a + -7a Combine like terms: 92 + -92 = 0 -92 + -7a + 4a2 = 0 + 7a + -7a -92 + -7a + 4a2 = 7a + -7a Combine like terms: 7a + -7a = 0 -92 + -7a + 4a2 = 0 Factor a trinomial. (-4 + -1a)(23 + -4a) = 0Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 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 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 2
Set the factor '(23 + -4a)' equal to zero and attempt to solve: Simplifying 23 + -4a = 0 Solving 23 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -4a = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -4a = 0 + -23 -4a = 0 + -23 Combine like terms: 0 + -23 = -23 -4a = -23 Divide each side by '-4'. a = 5.75 Simplifying a = 5.75Solution
a = {-4, 5.75}
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