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Simplifying (a + 5)(a + -5)(a2 + 25) = 0 Reorder the terms: (5 + a)(a + -5)(a2 + 25) = 0 Reorder the terms: (5 + a)(-5 + a)(a2 + 25) = 0 Reorder the terms: (5 + a)(-5 + a)(25 + a2) = 0 Multiply (5 + a) * (-5 + a) (5(-5 + a) + a(-5 + a))(25 + a2) = 0 ((-5 * 5 + a * 5) + a(-5 + a))(25 + a2) = 0 ((-25 + 5a) + a(-5 + a))(25 + a2) = 0 (-25 + 5a + (-5 * a + a * a))(25 + a2) = 0 (-25 + 5a + (-5a + a2))(25 + a2) = 0 Combine like terms: 5a + -5a = 0 (-25 + 0 + a2)(25 + a2) = 0 (-25 + a2)(25 + a2) = 0 Multiply (-25 + a2) * (25 + a2) (-25(25 + a2) + a2(25 + a2)) = 0 ((25 * -25 + a2 * -25) + a2(25 + a2)) = 0 ((-625 + -25a2) + a2(25 + a2)) = 0 (-625 + -25a2 + (25 * a2 + a2 * a2)) = 0 (-625 + -25a2 + (25a2 + a4)) = 0 Combine like terms: -25a2 + 25a2 = 0 (-625 + 0 + a4) = 0 (-625 + a4) = 0 Solving -625 + a4 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '625' to each side of the equation. -625 + 625 + a4 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + a4 = 0 + 625 a4 = 0 + 625 Combine like terms: 0 + 625 = 625 a4 = 625 Simplifying a4 = 625 Reorder the terms: -625 + a4 = 625 + -625 Combine like terms: 625 + -625 = 0 -625 + a4 = 0 Factor a difference between two squares. (25 + a2)(-25 + a2) = 0 Factor a difference between two squares. (25 + a2)((5 + a)(-5 + a)) = 0Subproblem 1
Set the factor '(25 + a2)' equal to zero and attempt to solve: Simplifying 25 + a2 = 0 Solving 25 + a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + a2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + a2 = 0 + -25 a2 = 0 + -25 Combine like terms: 0 + -25 = -25 a2 = -25 Simplifying a2 = -25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + a)' equal to zero and attempt to solve: Simplifying 5 + a = 0 Solving 5 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + a = 0 + -5 a = 0 + -5 Combine like terms: 0 + -5 = -5 a = -5 Simplifying a = -5Subproblem 3
Set the factor '(-5 + a)' equal to zero and attempt to solve: Simplifying -5 + a = 0 Solving -5 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + a = 0 + 5 a = 0 + 5 Combine like terms: 0 + 5 = 5 a = 5 Simplifying a = 5Solution
a = {-5, 5}
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