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Simplifying a4 = 104a2 + -400 Reorder the terms: a4 = -400 + 104a2 Solving a4 = -400 + 104a2 Solving for variable 'a'. Reorder the terms: 400 + -104a2 + a4 = -400 + 104a2 + 400 + -104a2 Reorder the terms: 400 + -104a2 + a4 = -400 + 400 + 104a2 + -104a2 Combine like terms: -400 + 400 = 0 400 + -104a2 + a4 = 0 + 104a2 + -104a2 400 + -104a2 + a4 = 104a2 + -104a2 Combine like terms: 104a2 + -104a2 = 0 400 + -104a2 + a4 = 0 Factor a trinomial. (4 + -1a2)(100 + -1a2) = 0 Factor a difference between two squares. ((2 + a)(2 + -1a))(100 + -1a2) = 0 Factor a difference between two squares. ((10 + a)(10 + -1a))(2 + a)(2 + -1a) = 0Subproblem 1
Set the factor '(2 + a)' equal to zero and attempt to solve: Simplifying 2 + a = 0 Solving 2 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a = 0 + -2 a = 0 + -2 Combine like terms: 0 + -2 = -2 a = -2 Simplifying a = -2Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Subproblem 3
Set the factor '(10 + a)' equal to zero and attempt to solve: Simplifying 10 + a = 0 Solving 10 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + a = 0 + -10 a = 0 + -10 Combine like terms: 0 + -10 = -10 a = -10 Simplifying a = -10Subproblem 4
Set the factor '(10 + -1a)' equal to zero and attempt to solve: Simplifying 10 + -1a = 0 Solving 10 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1a = 0 + -10 -1a = 0 + -10 Combine like terms: 0 + -10 = -10 -1a = -10 Divide each side by '-1'. a = 10 Simplifying a = 10Solution
a = {-2, 2, -10, 10}
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