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Simplifying X2 + 14 + y2 + 2y = 14 Reorder the terms: 14 + X2 + 2y + y2 = 14 Add '-14' to each side of the equation. 14 + X2 + 2y + -14 + y2 = 14 + -14 Reorder the terms: 14 + -14 + X2 + 2y + y2 = 14 + -14 Combine like terms: 14 + -14 = 0 0 + X2 + 2y + y2 = 14 + -14 X2 + 2y + y2 = 14 + -14 Combine like terms: 14 + -14 = 0 X2 + 2y + y2 = 0 Solving X2 + 2y + y2 = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2y' to each side of the equation. X2 + 2y + -2y + y2 = 0 + -2y Combine like terms: 2y + -2y = 0 X2 + 0 + y2 = 0 + -2y X2 + y2 = 0 + -2y Remove the zero: X2 + y2 = -2y Add '-1y2' to each side of the equation. X2 + y2 + -1y2 = -2y + -1y2 Combine like terms: y2 + -1y2 = 0 X2 + 0 = -2y + -1y2 X2 = -2y + -1y2 Simplifying X2 = -2y + -1y2 Reorder the terms: X2 + 2y + y2 = -2y + 2y + -1y2 + y2 Combine like terms: -2y + 2y = 0 X2 + 2y + y2 = 0 + -1y2 + y2 X2 + 2y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 X2 + 2y + y2 = 0 Factor a trinomial. (X + y)(X + y) = 0Subproblem 1
Set the factor '(X + y)' equal to zero and attempt to solve: Simplifying X + y = 0 Solving X + y = 0 Move all terms containing X to the left, all other terms to the right. Add '-1y' to each side of the equation. X + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 X + 0 = 0 + -1y X = 0 + -1y Remove the zero: X = -1y Simplifying X = -1ySubproblem 2
Set the factor '(X + y)' equal to zero and attempt to solve: Simplifying X + y = 0 Solving X + y = 0 Move all terms containing X to the left, all other terms to the right. Add '-1y' to each side of the equation. X + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 X + 0 = 0 + -1y X = 0 + -1y Remove the zero: X = -1y Simplifying X = -1ySolution
X = {-1y, -1y}
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