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Simplifying (x + y2)(x + -5y2) = 0 Multiply (x + y2) * (x + -5y2) (x(x + -5y2) + y2(x + -5y2)) = 0 ((x * x + -5y2 * x) + y2(x + -5y2)) = 0 Reorder the terms: ((-5xy2 + x2) + y2(x + -5y2)) = 0 ((-5xy2 + x2) + y2(x + -5y2)) = 0 (-5xy2 + x2 + (x * y2 + -5y2 * y2)) = 0 (-5xy2 + x2 + (xy2 + -5y4)) = 0 Reorder the terms: (-5xy2 + xy2 + x2 + -5y4) = 0 Combine like terms: -5xy2 + xy2 = -4xy2 (-4xy2 + x2 + -5y4) = 0 Solving -4xy2 + x2 + -5y4 = 0 Solving for variable 'x'. Factor a trinomial. (x + -5y2)(x + y2) = 0Subproblem 1
Set the factor '(x + -5y2)' equal to zero and attempt to solve: Simplifying x + -5y2 = 0 Solving x + -5y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '5y2' to each side of the equation. x + -5y2 + 5y2 = 0 + 5y2 Combine like terms: -5y2 + 5y2 = 0 x + 0 = 0 + 5y2 x = 0 + 5y2 Remove the zero: x = 5y2 Simplifying x = 5y2Subproblem 2
Set the factor '(x + y2)' equal to zero and attempt to solve: Simplifying x + y2 = 0 Solving x + y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. x + y2 + -1y2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 x + 0 = 0 + -1y2 x = 0 + -1y2 Remove the zero: x = -1y2 Simplifying x = -1y2Solution
x = {5y2, -1y2}
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