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Simplifying a(a + -5) = -7(a + -9) Reorder the terms: a(-5 + a) = -7(a + -9) (-5 * a + a * a) = -7(a + -9) (-5a + a2) = -7(a + -9) Reorder the terms: -5a + a2 = -7(-9 + a) -5a + a2 = (-9 * -7 + a * -7) -5a + a2 = (63 + -7a) Solving -5a + a2 = 63 + -7a Solving for variable 'a'. Reorder the terms: -63 + -5a + 7a + a2 = 63 + -7a + -63 + 7a Combine like terms: -5a + 7a = 2a -63 + 2a + a2 = 63 + -7a + -63 + 7a Reorder the terms: -63 + 2a + a2 = 63 + -63 + -7a + 7a Combine like terms: 63 + -63 = 0 -63 + 2a + a2 = 0 + -7a + 7a -63 + 2a + a2 = -7a + 7a Combine like terms: -7a + 7a = 0 -63 + 2a + a2 = 0 Factor a trinomial. (-9 + -1a)(7 + -1a) = 0Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve: Simplifying -9 + -1a = 0 Solving -9 + -1a = 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 + -1a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1a = 0 + 9 -1a = 0 + 9 Combine like terms: 0 + 9 = 9 -1a = 9 Divide each side by '-1'. a = -9 Simplifying a = -9Subproblem 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 = {-9, 7}
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