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Simplifying 48x2 + 48xy2 + 12y4 = 0 Reorder the terms: 48xy2 + 48x2 + 12y4 = 0 Solving 48xy2 + 48x2 + 12y4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(4xy2 + 4x2 + y4) = 0 Factor a trinomial. 12((2x + y2)(2x + y2)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(2x + y2)' equal to zero and attempt to solve: Simplifying 2x + y2 = 0 Solving 2x + y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. 2x + y2 + -1y2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 2x + 0 = 0 + -1y2 2x = 0 + -1y2 Remove the zero: 2x = -1y2 Divide each side by '2'. x = -0.5y2 Simplifying x = -0.5y2Subproblem 2
Set the factor '(2x + y2)' equal to zero and attempt to solve: Simplifying 2x + y2 = 0 Solving 2x + y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. 2x + y2 + -1y2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 2x + 0 = 0 + -1y2 2x = 0 + -1y2 Remove the zero: 2x = -1y2 Divide each side by '2'. x = -0.5y2 Simplifying x = -0.5y2Solution
x = {-0.5y2, -0.5y2}
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