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Simplifying 5y2 + 5y + 5y + 5x2 = 0 Reorder the terms: 5x2 + 5y + 5y + 5y2 = 0 Combine like terms: 5y + 5y = 10y 5x2 + 10y + 5y2 = 0 Solving 5x2 + 10y + 5y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10y' to each side of the equation. 5x2 + 10y + -10y + 5y2 = 0 + -10y Combine like terms: 10y + -10y = 0 5x2 + 0 + 5y2 = 0 + -10y 5x2 + 5y2 = 0 + -10y Remove the zero: 5x2 + 5y2 = -10y Add '-5y2' to each side of the equation. 5x2 + 5y2 + -5y2 = -10y + -5y2 Combine like terms: 5y2 + -5y2 = 0 5x2 + 0 = -10y + -5y2 5x2 = -10y + -5y2 Divide each side by '5'. 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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