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Simplifying 2x4 + -2ax2 + -4a2 = 0forx Reorder the terms: -2ax2 + -4a2 + 2x4 = 0forx Anything times zero is zero. -2ax2 + -4a2 + 2x4 = 0forx Solving -2ax2 + -4a2 + 2x4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1ax2 + -2a2 + x4) = 0 Factor a trinomial. 2((-1a + -1x2)(2a + -1x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1a + -1x2)' equal to zero and attempt to solve: Simplifying -1a + -1x2 = 0 Solving -1a + -1x2 = 0 Move all terms containing a to the left, all other terms to the right. Add 'x2' to each side of the equation. -1a + -1x2 + x2 = 0 + x2 Combine like terms: -1x2 + x2 = 0 -1a + 0 = 0 + x2 -1a = 0 + x2 Remove the zero: -1a = x2 Divide each side by '-1'. a = -1x2 Simplifying a = -1x2Subproblem 2
Set the factor '(2a + -1x2)' equal to zero and attempt to solve: Simplifying 2a + -1x2 = 0 Solving 2a + -1x2 = 0 Move all terms containing a to the left, all other terms to the right. Add 'x2' to each side of the equation. 2a + -1x2 + x2 = 0 + x2 Combine like terms: -1x2 + x2 = 0 2a + 0 = 0 + x2 2a = 0 + x2 Remove the zero: 2a = x2 Divide each side by '2'. a = 0.5x2 Simplifying a = 0.5x2Solution
a = {-1x2, 0.5x2}
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