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Simplifying z2 + -3za + -10a2 = 0 Reorder the terms: -3az + -10a2 + z2 = 0 Solving -3az + -10a2 + z2 = 0 Solving for variable 'a'. Factor a trinomial. (-2a + -1z)(5a + -1z) = 0Subproblem 1
Set the factor '(-2a + -1z)' equal to zero and attempt to solve: Simplifying -2a + -1z = 0 Solving -2a + -1z = 0 Move all terms containing a to the left, all other terms to the right. Add 'z' to each side of the equation. -2a + -1z + z = 0 + z Combine like terms: -1z + z = 0 -2a + 0 = 0 + z -2a = 0 + z Remove the zero: -2a = z Divide each side by '-2'. a = -0.5z Simplifying a = -0.5zSubproblem 2
Set the factor '(5a + -1z)' equal to zero and attempt to solve: Simplifying 5a + -1z = 0 Solving 5a + -1z = 0 Move all terms containing a to the left, all other terms to the right. Add 'z' to each side of the equation. 5a + -1z + z = 0 + z Combine like terms: -1z + z = 0 5a + 0 = 0 + z 5a = 0 + z Remove the zero: 5a = z Divide each side by '5'. a = 0.2z Simplifying a = 0.2zSolution
a = {-0.5z, 0.2z}
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