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Simplifying (5a + -1b)(5a + b) = 0 Multiply (5a + -1b) * (5a + b) (5a * (5a + b) + -1b * (5a + b)) = 0 ((5a * 5a + b * 5a) + -1b * (5a + b)) = 0 Reorder the terms: ((5ab + 25a2) + -1b * (5a + b)) = 0 ((5ab + 25a2) + -1b * (5a + b)) = 0 (5ab + 25a2 + (5a * -1b + b * -1b)) = 0 (5ab + 25a2 + (-5ab + -1b2)) = 0 Reorder the terms: (5ab + -5ab + 25a2 + -1b2) = 0 Combine like terms: 5ab + -5ab = 0 (0 + 25a2 + -1b2) = 0 (25a2 + -1b2) = 0 Solving 25a2 + -1b2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b2' to each side of the equation. 25a2 + -1b2 + b2 = 0 + b2 Combine like terms: -1b2 + b2 = 0 25a2 + 0 = 0 + b2 25a2 = 0 + b2 Remove the zero: 25a2 = b2 Divide each side by '25'. a2 = 0.04b2 Simplifying a2 = 0.04b2 Take the square root of each side: a = {-0.2b, 0.2b}
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