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Simplifying a(8a + 1) = 7 Reorder the terms: a(1 + 8a) = 7 (1 * a + 8a * a) = 7 (1a + 8a2) = 7 Solving 1a + 8a2 = 7 Solving for variable 'a'. Reorder the terms: -7 + 1a + 8a2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 1a + 8a2 = 0 Factor a trinomial. (-1 + -1a)(7 + -8a) = 0Subproblem 1
Set the factor '(-1 + -1a)' equal to zero and attempt to solve: Simplifying -1 + -1a = 0 Solving -1 + -1a = 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 + -1a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1a = 0 + 1 -1a = 0 + 1 Combine like terms: 0 + 1 = 1 -1a = 1 Divide each side by '-1'. a = -1 Simplifying a = -1Subproblem 2
Set the factor '(7 + -8a)' equal to zero and attempt to solve: Simplifying 7 + -8a = 0 Solving 7 + -8a = 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 + -8a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8a = 0 + -7 -8a = 0 + -7 Combine like terms: 0 + -7 = -7 -8a = -7 Divide each side by '-8'. a = 0.875 Simplifying a = 0.875Solution
a = {-1, 0.875}
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