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Simplifying (5a + -2b)(7a + -4b) = 0 Multiply (5a + -2b) * (7a + -4b) (5a * (7a + -4b) + -2b * (7a + -4b)) = 0 ((7a * 5a + -4b * 5a) + -2b * (7a + -4b)) = 0 Reorder the terms: ((-20ab + 35a2) + -2b * (7a + -4b)) = 0 ((-20ab + 35a2) + -2b * (7a + -4b)) = 0 (-20ab + 35a2 + (7a * -2b + -4b * -2b)) = 0 (-20ab + 35a2 + (-14ab + 8b2)) = 0 Reorder the terms: (-20ab + -14ab + 35a2 + 8b2) = 0 Combine like terms: -20ab + -14ab = -34ab (-34ab + 35a2 + 8b2) = 0 Solving -34ab + 35a2 + 8b2 = 0 Solving for variable 'a'. Factor a trinomial. (7a + -4b)(5a + -2b) = 0Subproblem 1
Set the factor '(7a + -4b)' equal to zero and attempt to solve: Simplifying 7a + -4b = 0 Solving 7a + -4b = 0 Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 7a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 7a + 0 = 0 + 4b 7a = 0 + 4b Remove the zero: 7a = 4b Divide each side by '7'. a = 0.5714285714b Simplifying a = 0.5714285714bSubproblem 2
Set the factor '(5a + -2b)' equal to zero and attempt to solve: Simplifying 5a + -2b = 0 Solving 5a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 5a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 5a + 0 = 0 + 2b 5a = 0 + 2b Remove the zero: 5a = 2b Divide each side by '5'. a = 0.4b Simplifying a = 0.4bSolution
a = {0.5714285714b, 0.4b}
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