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