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Simplifying (4a + -1b)(a + -5b) = 0 Multiply (4a + -1b) * (a + -5b) (4a * (a + -5b) + -1b * (a + -5b)) = 0 ((a * 4a + -5b * 4a) + -1b * (a + -5b)) = 0 Reorder the terms: ((-20ab + 4a2) + -1b * (a + -5b)) = 0 ((-20ab + 4a2) + -1b * (a + -5b)) = 0 (-20ab + 4a2 + (a * -1b + -5b * -1b)) = 0 (-20ab + 4a2 + (-1ab + 5b2)) = 0 Reorder the terms: (-20ab + -1ab + 4a2 + 5b2) = 0 Combine like terms: -20ab + -1ab = -21ab (-21ab + 4a2 + 5b2) = 0 Solving -21ab + 4a2 + 5b2 = 0 Solving for variable 'a'. Factor a trinomial. (a + -5b)(4a + -1b) = 0Subproblem 1
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 = 5bSubproblem 2
Set the factor '(4a + -1b)' equal to zero and attempt to solve: Simplifying 4a + -1b = 0 Solving 4a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 4a + -1b + b = 0 + b Combine like terms: -1b + b = 0 4a + 0 = 0 + b 4a = 0 + b Remove the zero: 4a = b Divide each side by '4'. a = 0.25b Simplifying a = 0.25bSolution
a = {5b, 0.25b}
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