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Simplifying y2 = 2y + -1x2 Reorder the terms: y2 = -1x2 + 2y Solving y2 = -1x2 + 2y Solving for variable 'y'. Reorder the terms: x2 + -2y + y2 = -1x2 + 2y + x2 + -2y Reorder the terms: x2 + -2y + y2 = -1x2 + x2 + 2y + -2y Combine like terms: -1x2 + x2 = 0 x2 + -2y + y2 = 0 + 2y + -2y x2 + -2y + y2 = 2y + -2y Combine like terms: 2y + -2y = 0 x2 + -2y + y2 = 0 Factor a trinomial. (x + -1y)(x + -1y) = 0Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Divide each side by '-1'. y = x Simplifying y = xSubproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Divide each side by '-1'. y = x Simplifying y = xSolution
y = {x, x}
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