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Simplifying (2a + b)(1a + 5b) = 0 Multiply (2a + b) * (1a + 5b) (2a * (1a + 5b) + b(1a + 5b)) = 0 ((1a * 2a + 5b * 2a) + b(1a + 5b)) = 0 Reorder the terms: ((10ab + 2a2) + b(1a + 5b)) = 0 ((10ab + 2a2) + b(1a + 5b)) = 0 (10ab + 2a2 + (1a * b + 5b * b)) = 0 (10ab + 2a2 + (1ab + 5b2)) = 0 Reorder the terms: (10ab + 1ab + 2a2 + 5b2) = 0 Combine like terms: 10ab + 1ab = 11ab (11ab + 2a2 + 5b2) = 0 Solving 11ab + 2a2 + 5b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + b)(a + 5b) = 0Subproblem 1
Set the factor '(2a + b)' equal to zero and attempt to solve: Simplifying 2a + b = 0 Solving 2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5bSubproblem 2
Set the factor '(a + 5b)' equal to zero and attempt to solve: Simplifying a + 5b = 0 Solving a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 a + 0 = 0 + -5b a = 0 + -5b Remove the zero: a = -5b Simplifying a = -5bSolution
a = {-0.5b, -5b}
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