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Simplifying (5a + -1b)(9a + 2b) = 0 Multiply (5a + -1b) * (9a + 2b) (5a * (9a + 2b) + -1b * (9a + 2b)) = 0 ((9a * 5a + 2b * 5a) + -1b * (9a + 2b)) = 0 Reorder the terms: ((10ab + 45a2) + -1b * (9a + 2b)) = 0 ((10ab + 45a2) + -1b * (9a + 2b)) = 0 (10ab + 45a2 + (9a * -1b + 2b * -1b)) = 0 (10ab + 45a2 + (-9ab + -2b2)) = 0 Reorder the terms: (10ab + -9ab + 45a2 + -2b2) = 0 Combine like terms: 10ab + -9ab = 1ab (1ab + 45a2 + -2b2) = 0 Solving 1ab + 45a2 + -2b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -1b)(9a + 2b) = 0Subproblem 1
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 = 0.2bSubproblem 2
Set the factor '(9a + 2b)' equal to zero and attempt to solve: Simplifying 9a + 2b = 0 Solving 9a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 9a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 9a + 0 = 0 + -2b 9a = 0 + -2b Remove the zero: 9a = -2b Divide each side by '9'. a = -0.2222222222b Simplifying a = -0.2222222222bSolution
a = {0.2b, -0.2222222222b}
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