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Simplifying 2a2 + -4ab + 5ab + -10b2 = 0 Reorder the terms: -4ab + 5ab + 2a2 + -10b2 = 0 Combine like terms: -4ab + 5ab = 1ab 1ab + 2a2 + -10b2 = 0 Solving 1ab + 2a2 + -10b2 = 0 Solving for variable 'a'. Factor a trinomial. (a + -2b)(2a + 5b) = 0Subproblem 1
Set the factor '(a + -2b)' equal to zero and attempt to solve: Simplifying a + -2b = 0 Solving a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 a + 0 = 0 + 2b a = 0 + 2b Remove the zero: a = 2b Simplifying a = 2bSubproblem 2
Set the factor '(2a + 5b)' equal to zero and attempt to solve: Simplifying 2a + 5b = 0 Solving 2a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 2a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 2a + 0 = 0 + -5b 2a = 0 + -5b Remove the zero: 2a = -5b Divide each side by '2'. a = -2.5b Simplifying a = -2.5bSolution
a = {2b, -2.5b}
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