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Simplifying 2a2 + -5ac + 3c2 = 0 Reorder the terms: -5ac + 2a2 + 3c2 = 0 Solving -5ac + 2a2 + 3c2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -3c)(a + -1c) = 0Subproblem 1
Set the factor '(2a + -3c)' equal to zero and attempt to solve: Simplifying 2a + -3c = 0 Solving 2a + -3c = 0 Move all terms containing a to the left, all other terms to the right. Add '3c' to each side of the equation. 2a + -3c + 3c = 0 + 3c Combine like terms: -3c + 3c = 0 2a + 0 = 0 + 3c 2a = 0 + 3c Remove the zero: 2a = 3c Divide each side by '2'. a = 1.5c Simplifying a = 1.5cSubproblem 2
Set the factor '(a + -1c)' equal to zero and attempt to solve: Simplifying a + -1c = 0 Solving a + -1c = 0 Move all terms containing a to the left, all other terms to the right. Add 'c' to each side of the equation. a + -1c + c = 0 + c Combine like terms: -1c + c = 0 a + 0 = 0 + c a = 0 + c Remove the zero: a = c Simplifying a = cSolution
a = {1.5c, c}
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