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Simplifying (a + -7)(2a + -9) = 0 Reorder the terms: (-7 + a)(2a + -9) = 0 Reorder the terms: (-7 + a)(-9 + 2a) = 0 Multiply (-7 + a) * (-9 + 2a) (-7(-9 + 2a) + a(-9 + 2a)) = 0 ((-9 * -7 + 2a * -7) + a(-9 + 2a)) = 0 ((63 + -14a) + a(-9 + 2a)) = 0 (63 + -14a + (-9 * a + 2a * a)) = 0 (63 + -14a + (-9a + 2a2)) = 0 Combine like terms: -14a + -9a = -23a (63 + -23a + 2a2) = 0 Solving 63 + -23a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (9 + -2a)(7 + -1a) = 0Subproblem 1
Set the factor '(9 + -2a)' equal to zero and attempt to solve: Simplifying 9 + -2a = 0 Solving 9 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2a = 0 + -9 -2a = 0 + -9 Combine like terms: 0 + -9 = -9 -2a = -9 Divide each side by '-2'. a = 4.5 Simplifying a = 4.5Subproblem 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 = {4.5, 7}
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