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Simplifying 2x2P2 + 2xyP + -4y2 = 0 Reorder the terms: 2xyP + 2x2P2 + -4y2 = 0 Solving 2xyP + 2x2P2 + -4y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(xyP + x2P2 + -2y2) = 0 Factor a trinomial. 2((xP + -1y)(xP + 2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(xP + -1y)' equal to zero and attempt to solve: Simplifying xP + -1y = 0 Solving xP + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. xP + -1y + y = 0 + y Combine like terms: -1y + y = 0 xP + 0 = 0 + y xP = 0 + y Remove the zero: xP = y Divide each side by 'P'. x = yP-1 Simplifying x = yP-1Subproblem 2
Set the factor '(xP + 2y)' equal to zero and attempt to solve: Simplifying xP + 2y = 0 Solving xP + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. xP + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 xP + 0 = 0 + -2y xP = 0 + -2y Remove the zero: xP = -2y Divide each side by 'P'. x = -2yP-1 Simplifying x = -2yP-1Solution
x = {yP-1, -2yP-1}
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