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Simplifying 0 = 5a2 + -6ab + -32b2 Reorder the terms: 0 = -6ab + 5a2 + -32b2 Solving 0 = -6ab + 5a2 + -32b2 Solving for variable 'a'. Remove the zero: 6ab + -5a2 + 32b2 = -6ab + 5a2 + -32b2 + 6ab + -5a2 + 32b2 Reorder the terms: 6ab + -5a2 + 32b2 = -6ab + 6ab + 5a2 + -5a2 + -32b2 + 32b2 Combine like terms: -6ab + 6ab = 0 6ab + -5a2 + 32b2 = 0 + 5a2 + -5a2 + -32b2 + 32b2 6ab + -5a2 + 32b2 = 5a2 + -5a2 + -32b2 + 32b2 Combine like terms: 5a2 + -5a2 = 0 6ab + -5a2 + 32b2 = 0 + -32b2 + 32b2 6ab + -5a2 + 32b2 = -32b2 + 32b2 Combine like terms: -32b2 + 32b2 = 0 6ab + -5a2 + 32b2 = 0 Factor a trinomial. (-1a + -2b)(5a + -16b) = 0Subproblem 1
Set the factor '(-1a + -2b)' equal to zero and attempt to solve: Simplifying -1a + -2b = 0 Solving -1a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. -1a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 -1a + 0 = 0 + 2b -1a = 0 + 2b Remove the zero: -1a = 2b Divide each side by '-1'. a = -2b Simplifying a = -2bSubproblem 2
Set the factor '(5a + -16b)' equal to zero and attempt to solve: Simplifying 5a + -16b = 0 Solving 5a + -16b = 0 Move all terms containing a to the left, all other terms to the right. Add '16b' to each side of the equation. 5a + -16b + 16b = 0 + 16b Combine like terms: -16b + 16b = 0 5a + 0 = 0 + 16b 5a = 0 + 16b Remove the zero: 5a = 16b Divide each side by '5'. a = 3.2b Simplifying a = 3.2bSolution
a = {-2b, 3.2b}
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