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Simplifying x2 + 10 + 9y2 = 0 Reorder the terms: 10 + x2 + 9y2 = 0 Solving 10 + x2 + 9y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + x2 + -10 + 9y2 = 0 + -10 Reorder the terms: 10 + -10 + x2 + 9y2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x2 + 9y2 = 0 + -10 x2 + 9y2 = 0 + -10 Combine like terms: 0 + -10 = -10 x2 + 9y2 = -10 Add '-9y2' to each side of the equation. x2 + 9y2 + -9y2 = -10 + -9y2 Combine like terms: 9y2 + -9y2 = 0 x2 + 0 = -10 + -9y2 x2 = -10 + -9y2 Simplifying x2 = -10 + -9y2 Reorder the terms: 10 + x2 + 9y2 = -10 + -9y2 + 10 + 9y2 Reorder the terms: 10 + x2 + 9y2 = -10 + 10 + -9y2 + 9y2 Combine like terms: -10 + 10 = 0 10 + x2 + 9y2 = 0 + -9y2 + 9y2 10 + x2 + 9y2 = -9y2 + 9y2 Combine like terms: -9y2 + 9y2 = 0 10 + x2 + 9y2 = 0 Factor a trinomial. (x + y)(x + 9y) = 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 + 9y)' equal to zero and attempt to solve: Simplifying x + 9y = 0 Solving x + 9y = 0 Move all terms containing x to the left, all other terms to the right. Add '-9y' to each side of the equation. x + 9y + -9y = 0 + -9y Combine like terms: 9y + -9y = 0 x + 0 = 0 + -9y x = 0 + -9y Remove the zero: x = -9y Simplifying x = -9ySolution
x = {-1y, -9y}
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