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Simplifying 0 = -1a3 + 49a Reorder the terms: 0 = 49a + -1a3 Solving 0 = 49a + -1a3 Solving for variable 'a'. Remove the zero: -49a + a3 = 49a + -1a3 + -49a + a3 Reorder the terms: -49a + a3 = 49a + -49a + -1a3 + a3 Combine like terms: 49a + -49a = 0 -49a + a3 = 0 + -1a3 + a3 -49a + a3 = -1a3 + a3 Combine like terms: -1a3 + a3 = 0 -49a + a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-49 + a2) = 0 Factor a difference between two squares. a((7 + a)(-7 + a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(7 + a)' equal to zero and attempt to solve: Simplifying 7 + a = 0 Solving 7 + a = 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 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7Subproblem 3
Set the factor '(-7 + a)' equal to zero and attempt to solve: Simplifying -7 + a = 0 Solving -7 + a = 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 + a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + a = 0 + 7 a = 0 + 7 Combine like terms: 0 + 7 = 7 a = 7 Simplifying a = 7Solution
a = {0, -7, 7}
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