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Simplifying X2 + 25 + Y2 + 9 = 36 Reorder the terms: 25 + 9 + X2 + Y2 = 36 Combine like terms: 25 + 9 = 34 34 + X2 + Y2 = 36 Solving 34 + X2 + Y2 = 36 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + X2 + -34 + Y2 = 36 + -34 Reorder the terms: 34 + -34 + X2 + Y2 = 36 + -34 Combine like terms: 34 + -34 = 0 0 + X2 + Y2 = 36 + -34 X2 + Y2 = 36 + -34 Combine like terms: 36 + -34 = 2 X2 + Y2 = 2 Add '-1Y2' to each side of the equation. X2 + Y2 + -1Y2 = 2 + -1Y2 Combine like terms: Y2 + -1Y2 = 0 X2 + 0 = 2 + -1Y2 X2 = 2 + -1Y2 Simplifying X2 = 2 + -1Y2 Reorder the terms: -2 + X2 + Y2 = 2 + -1Y2 + -2 + Y2 Reorder the terms: -2 + X2 + Y2 = 2 + -2 + -1Y2 + Y2 Combine like terms: 2 + -2 = 0 -2 + X2 + Y2 = 0 + -1Y2 + Y2 -2 + X2 + Y2 = -1Y2 + Y2 Combine like terms: -1Y2 + Y2 = 0 -2 + X2 + 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 X to the left, all other terms to the right. Add 'Y' to each side of the equation. X + -1Y + Y = 0 + Y Combine like terms: -1Y + Y = 0 X + 0 = 0 + Y X = 0 + Y Remove the zero: X = Y Simplifying X = YSubproblem 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 X to the left, all other terms to the right. Add 'Y' to each side of the equation. X + -1Y + Y = 0 + Y Combine like terms: -1Y + Y = 0 X + 0 = 0 + Y X = 0 + Y Remove the zero: X = Y Simplifying X = YSolution
X = {Y, Y}
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