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Simplifying 10a2 + -25ab + -2ab + 5b2 = 0 Reorder the terms: -25ab + -2ab + 10a2 + 5b2 = 0 Combine like terms: -25ab + -2ab = -27ab -27ab + 10a2 + 5b2 = 0 Solving -27ab + 10a2 + 5b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -5b)(5a + -1b) = 0Subproblem 1
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 = 2.5bSubproblem 2
Set the factor '(5a + -1b)' equal to zero and attempt to solve: Simplifying 5a + -1b = 0 Solving 5a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 5a + -1b + b = 0 + b Combine like terms: -1b + b = 0 5a + 0 = 0 + b 5a = 0 + b Remove the zero: 5a = b Divide each side by '5'. a = 0.2b Simplifying a = 0.2bSolution
a = {2.5b, 0.2b}
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