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