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Simplifying (4a + -3b)(4a + -3b) = 0 Multiply (4a + -3b) * (4a + -3b) (4a * (4a + -3b) + -3b * (4a + -3b)) = 0 ((4a * 4a + -3b * 4a) + -3b * (4a + -3b)) = 0 Reorder the terms: ((-12ab + 16a2) + -3b * (4a + -3b)) = 0 ((-12ab + 16a2) + -3b * (4a + -3b)) = 0 (-12ab + 16a2 + (4a * -3b + -3b * -3b)) = 0 (-12ab + 16a2 + (-12ab + 9b2)) = 0 Reorder the terms: (-12ab + -12ab + 16a2 + 9b2) = 0 Combine like terms: -12ab + -12ab = -24ab (-24ab + 16a2 + 9b2) = 0 Solving -24ab + 16a2 + 9b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -3b)(4a + -3b) = 0Subproblem 1
Set the factor '(4a + -3b)' equal to zero and attempt to solve: Simplifying 4a + -3b = 0 Solving 4a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 4a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 4a + 0 = 0 + 3b 4a = 0 + 3b Remove the zero: 4a = 3b Divide each side by '4'. a = 0.75b Simplifying a = 0.75bSubproblem 2
Set the factor '(4a + -3b)' equal to zero and attempt to solve: Simplifying 4a + -3b = 0 Solving 4a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 4a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 4a + 0 = 0 + 3b 4a = 0 + 3b Remove the zero: 4a = 3b Divide each side by '4'. a = 0.75b Simplifying a = 0.75bSolution
a = {0.75b, 0.75b}
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