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Simplifying 2a2 = 13a + 7 Reorder the terms: 2a2 = 7 + 13a Solving 2a2 = 7 + 13a Solving for variable 'a'. Reorder the terms: -7 + -13a + 2a2 = 7 + 13a + -7 + -13a Reorder the terms: -7 + -13a + 2a2 = 7 + -7 + 13a + -13a Combine like terms: 7 + -7 = 0 -7 + -13a + 2a2 = 0 + 13a + -13a -7 + -13a + 2a2 = 13a + -13a Combine like terms: 13a + -13a = 0 -7 + -13a + 2a2 = 0 Factor a trinomial. (-1 + -2a)(7 + -1a) = 0Subproblem 1
Set the factor '(-1 + -2a)' equal to zero and attempt to solve: Simplifying -1 + -2a = 0 Solving -1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2a = 0 + 1 -2a = 0 + 1 Combine like terms: 0 + 1 = 1 -2a = 1 Divide each side by '-2'. a = -0.5 Simplifying a = -0.5Subproblem 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 = {-0.5, 7}
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