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Simplifying (4a + -1b)(5a + -1b) = 0 Multiply (4a + -1b) * (5a + -1b) (4a * (5a + -1b) + -1b * (5a + -1b)) = 0 ((5a * 4a + -1b * 4a) + -1b * (5a + -1b)) = 0 Reorder the terms: ((-4ab + 20a2) + -1b * (5a + -1b)) = 0 ((-4ab + 20a2) + -1b * (5a + -1b)) = 0 (-4ab + 20a2 + (5a * -1b + -1b * -1b)) = 0 (-4ab + 20a2 + (-5ab + 1b2)) = 0 Reorder the terms: (-4ab + -5ab + 20a2 + 1b2) = 0 Combine like terms: -4ab + -5ab = -9ab (-9ab + 20a2 + 1b2) = 0 Solving -9ab + 20a2 + 1b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -1b)(5a + -1b) = 0Subproblem 1
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 = 0.25bSubproblem 2
Set the factor '(5a + -1b)' equal to zero and attempt to solve: Simplifying 5a + -1b = 0 Solving 5a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 5a + -1b + b = 0 + b Combine like terms: -1b + b = 0 5a + 0 = 0 + b 5a = 0 + b Remove the zero: 5a = b Divide each side by '5'. a = 0.2b Simplifying a = 0.2bSolution
a = {0.25b, 0.2b}
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