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Simplifying 4a2 + 3a = 52 Reorder the terms: 3a + 4a2 = 52 Solving 3a + 4a2 = 52 Solving for variable 'a'. Reorder the terms: -52 + 3a + 4a2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 3a + 4a2 = 0 Factor a trinomial. (-4 + -1a)(13 + -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 '(13 + -4a)' equal to zero and attempt to solve: Simplifying 13 + -4a = 0 Solving 13 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -4a = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -4a = 0 + -13 -4a = 0 + -13 Combine like terms: 0 + -13 = -13 -4a = -13 Divide each side by '-4'. a = 3.25 Simplifying a = 3.25Solution
a = {-4, 3.25}
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