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Simplifying 2(a2 + b2) = 5ab (a2 * 2 + b2 * 2) = 5ab (2a2 + 2b2) = 5ab Solving 2a2 + 2b2 = 5ab Solving for variable 'a'. Reorder the terms: -5ab + 2a2 + 2b2 = 5ab + -5ab Combine like terms: 5ab + -5ab = 0 -5ab + 2a2 + 2b2 = 0 Factor a trinomial. (a + -2b)(2a + -1b) = 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 + -1b)' equal to zero and attempt to solve: Simplifying 2a + -1b = 0 Solving 2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5bSolution
a = {2b, 0.5b}
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