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Simplifying (2a + -1b)(2a + -1b) = 0 Multiply (2a + -1b) * (2a + -1b) (2a * (2a + -1b) + -1b * (2a + -1b)) = 0 ((2a * 2a + -1b * 2a) + -1b * (2a + -1b)) = 0 Reorder the terms: ((-2ab + 4a2) + -1b * (2a + -1b)) = 0 ((-2ab + 4a2) + -1b * (2a + -1b)) = 0 (-2ab + 4a2 + (2a * -1b + -1b * -1b)) = 0 (-2ab + 4a2 + (-2ab + 1b2)) = 0 Reorder the terms: (-2ab + -2ab + 4a2 + 1b2) = 0 Combine like terms: -2ab + -2ab = -4ab (-4ab + 4a2 + 1b2) = 0 Solving -4ab + 4a2 + 1b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -1b)(2a + -1b) = 0Subproblem 1
Set the factor '(2a + -1b)' equal to zero and attempt to solve: Simplifying 2a + -1b = 0 Solving 2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5bSubproblem 2
Set the factor '(2a + -1b)' equal to zero and attempt to solve: Simplifying 2a + -1b = 0 Solving 2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5bSolution
a = {0.5b, 0.5b}
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