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Simplifying 2a(4a + 13) = 57 Reorder the terms: 2a(13 + 4a) = 57 (13 * 2a + 4a * 2a) = 57 (26a + 8a2) = 57 Solving 26a + 8a2 = 57 Solving for variable 'a'. Reorder the terms: -57 + 26a + 8a2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + 26a + 8a2 = 0 Factor a trinomial. (-19 + -4a)(3 + -2a) = 0Subproblem 1
Set the factor '(-19 + -4a)' equal to zero and attempt to solve: Simplifying -19 + -4a = 0 Solving -19 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -4a = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -4a = 0 + 19 -4a = 0 + 19 Combine like terms: 0 + 19 = 19 -4a = 19 Divide each side by '-4'. a = -4.75 Simplifying a = -4.75Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {-4.75, 1.5}
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