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Simplifying (a + -3)(a + 7) + (a + -3)(a + 4) = 0 Reorder the terms: (-3 + a)(a + 7) + (a + -3)(a + 4) = 0 Reorder the terms: (-3 + a)(7 + a) + (a + -3)(a + 4) = 0 Multiply (-3 + a) * (7 + a) (-3(7 + a) + a(7 + a)) + (a + -3)(a + 4) = 0 ((7 * -3 + a * -3) + a(7 + a)) + (a + -3)(a + 4) = 0 ((-21 + -3a) + a(7 + a)) + (a + -3)(a + 4) = 0 (-21 + -3a + (7 * a + a * a)) + (a + -3)(a + 4) = 0 (-21 + -3a + (7a + a2)) + (a + -3)(a + 4) = 0 Combine like terms: -3a + 7a = 4a (-21 + 4a + a2) + (a + -3)(a + 4) = 0 Reorder the terms: -21 + 4a + a2 + (-3 + a)(a + 4) = 0 Reorder the terms: -21 + 4a + a2 + (-3 + a)(4 + a) = 0 Multiply (-3 + a) * (4 + a) -21 + 4a + a2 + (-3(4 + a) + a(4 + a)) = 0 -21 + 4a + a2 + ((4 * -3 + a * -3) + a(4 + a)) = 0 -21 + 4a + a2 + ((-12 + -3a) + a(4 + a)) = 0 -21 + 4a + a2 + (-12 + -3a + (4 * a + a * a)) = 0 -21 + 4a + a2 + (-12 + -3a + (4a + a2)) = 0 Combine like terms: -3a + 4a = 1a -21 + 4a + a2 + (-12 + 1a + a2) = 0 Reorder the terms: -21 + -12 + 4a + 1a + a2 + a2 = 0 Combine like terms: -21 + -12 = -33 -33 + 4a + 1a + a2 + a2 = 0 Combine like terms: 4a + 1a = 5a -33 + 5a + a2 + a2 = 0 Combine like terms: a2 + a2 = 2a2 -33 + 5a + 2a2 = 0 Solving -33 + 5a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-11 + -2a)(3 + -1a) = 0Subproblem 1
Set the factor '(-11 + -2a)' equal to zero and attempt to solve: Simplifying -11 + -2a = 0 Solving -11 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2a = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2a = 0 + 11 -2a = 0 + 11 Combine like terms: 0 + 11 = 11 -2a = 11 Divide each side by '-2'. a = -5.5 Simplifying a = -5.5Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-5.5, 3}
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