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Simplifying x2 + 10y + 25y2 = 0 Solving x2 + 10y + 25y2 = 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. x2 + 10y + -10y + 25y2 = 0 + -10y Combine like terms: 10y + -10y = 0 x2 + 0 + 25y2 = 0 + -10y x2 + 25y2 = 0 + -10y Remove the zero: x2 + 25y2 = -10y Add '-25y2' to each side of the equation. x2 + 25y2 + -25y2 = -10y + -25y2 Combine like terms: 25y2 + -25y2 = 0 x2 + 0 = -10y + -25y2 x2 = -10y + -25y2 Simplifying x2 = -10y + -25y2 Reorder the terms: x2 + 10y + 25y2 = -10y + 10y + -25y2 + 25y2 Combine like terms: -10y + 10y = 0 x2 + 10y + 25y2 = 0 + -25y2 + 25y2 x2 + 10y + 25y2 = -25y2 + 25y2 Combine like terms: -25y2 + 25y2 = 0 x2 + 10y + 25y2 = 0 Factor a trinomial. (x + 5y)(x + 5y) = 0Subproblem 1
Set the factor '(x + 5y)' equal to zero and attempt to solve: Simplifying x + 5y = 0 Solving x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 x + 0 = 0 + -5y x = 0 + -5y Remove the zero: x = -5y Simplifying x = -5ySubproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve: Simplifying x + 5y = 0 Solving x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 x + 0 = 0 + -5y x = 0 + -5y Remove the zero: x = -5y Simplifying x = -5ySolution
x = {-5y, -5y}
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