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Simplifying 30c2 + 19ca + -63a2 = 0 Reorder the terms: 19ac + -63a2 + 30c2 = 0 Solving 19ac + -63a2 + 30c2 = 0 Solving for variable 'a'. Factor a trinomial. (-9a + -5c)(7a + -6c) = 0Subproblem 1
Set the factor '(-9a + -5c)' equal to zero and attempt to solve: Simplifying -9a + -5c = 0 Solving -9a + -5c = 0 Move all terms containing a to the left, all other terms to the right. Add '5c' to each side of the equation. -9a + -5c + 5c = 0 + 5c Combine like terms: -5c + 5c = 0 -9a + 0 = 0 + 5c -9a = 0 + 5c Remove the zero: -9a = 5c Divide each side by '-9'. a = -0.5555555556c Simplifying a = -0.5555555556cSubproblem 2
Set the factor '(7a + -6c)' equal to zero and attempt to solve: Simplifying 7a + -6c = 0 Solving 7a + -6c = 0 Move all terms containing a to the left, all other terms to the right. Add '6c' to each side of the equation. 7a + -6c + 6c = 0 + 6c Combine like terms: -6c + 6c = 0 7a + 0 = 0 + 6c 7a = 0 + 6c Remove the zero: 7a = 6c Divide each side by '7'. a = 0.8571428571c Simplifying a = 0.8571428571cSolution
a = {-0.5555555556c, 0.8571428571c}
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