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Simplifying ax2 = a + a2 Solving ax2 = a + a2 Solving for variable 'a'. Reorder the terms: -1a + ax2 + -1a2 = a + a2 + -1a + -1a2 Reorder the terms: -1a + ax2 + -1a2 = a + -1a + a2 + -1a2 Combine like terms: a + -1a = 0 -1a + ax2 + -1a2 = 0 + a2 + -1a2 -1a + ax2 + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -1a + ax2 + -1a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-1 + x2 + -1a) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-1 + x2 + -1a)' equal to zero and attempt to solve: Simplifying -1 + x2 + -1a = 0 Reorder the terms: -1 + -1a + x2 = 0 Solving -1 + -1a + x2 = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1a + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1a + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1a + x2 = 0 + 1 -1a + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1a + x2 = 1 Add '-1x2' to each side of the equation. -1a + x2 + -1x2 = 1 + -1x2 Combine like terms: x2 + -1x2 = 0 -1a + 0 = 1 + -1x2 -1a = 1 + -1x2 Divide each side by '-1'. a = -1 + x2 Simplifying a = -1 + x2Solution
a = {0, -1 + x2}
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