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Simplifying (5a + -4b)(5a + -4b) = 0 Multiply (5a + -4b) * (5a + -4b) (5a * (5a + -4b) + -4b * (5a + -4b)) = 0 ((5a * 5a + -4b * 5a) + -4b * (5a + -4b)) = 0 Reorder the terms: ((-20ab + 25a2) + -4b * (5a + -4b)) = 0 ((-20ab + 25a2) + -4b * (5a + -4b)) = 0 (-20ab + 25a2 + (5a * -4b + -4b * -4b)) = 0 (-20ab + 25a2 + (-20ab + 16b2)) = 0 Reorder the terms: (-20ab + -20ab + 25a2 + 16b2) = 0 Combine like terms: -20ab + -20ab = -40ab (-40ab + 25a2 + 16b2) = 0 Solving -40ab + 25a2 + 16b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -4b)(5a + -4b) = 0Subproblem 1
Set the factor '(5a + -4b)' equal to zero and attempt to solve: Simplifying 5a + -4b = 0 Solving 5a + -4b = 0 Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 5a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 5a + 0 = 0 + 4b 5a = 0 + 4b Remove the zero: 5a = 4b Divide each side by '5'. a = 0.8b Simplifying a = 0.8bSubproblem 2
Set the factor '(5a + -4b)' equal to zero and attempt to solve: Simplifying 5a + -4b = 0 Solving 5a + -4b = 0 Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 5a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 5a + 0 = 0 + 4b 5a = 0 + 4b Remove the zero: 5a = 4b Divide each side by '5'. a = 0.8b Simplifying a = 0.8bSolution
a = {0.8b, 0.8b}
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