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Simplifying (2a + 1)(a + -7) = 0 Reorder the terms: (1 + 2a)(a + -7) = 0 Reorder the terms: (1 + 2a)(-7 + a) = 0 Multiply (1 + 2a) * (-7 + a) (1(-7 + a) + 2a * (-7 + a)) = 0 ((-7 * 1 + a * 1) + 2a * (-7 + a)) = 0 ((-7 + 1a) + 2a * (-7 + a)) = 0 (-7 + 1a + (-7 * 2a + a * 2a)) = 0 (-7 + 1a + (-14a + 2a2)) = 0 Combine like terms: 1a + -14a = -13a (-7 + -13a + 2a2) = 0 Solving -7 + -13a + 2a2 = 0 Solving for variable 'a'. 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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