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