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Simplifying x2 + -30y2 = -1 Solving x2 + -30y2 = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30y2' to each side of the equation. x2 + -30y2 + 30y2 = -1 + 30y2 Combine like terms: -30y2 + 30y2 = 0 x2 + 0 = -1 + 30y2 x2 = -1 + 30y2 Simplifying x2 = -1 + 30y2 Reorder the terms: 1 + x2 + -30y2 = -1 + 30y2 + 1 + -30y2 Reorder the terms: 1 + x2 + -30y2 = -1 + 1 + 30y2 + -30y2 Combine like terms: -1 + 1 = 0 1 + x2 + -30y2 = 0 + 30y2 + -30y2 1 + x2 + -30y2 = 30y2 + -30y2 Combine like terms: 30y2 + -30y2 = 0 1 + x2 + -30y2 = 0 Factor a trinomial. (x + -5y)(x + 6y) = 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 + 6y)' equal to zero and attempt to solve: Simplifying x + 6y = 0 Solving x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 x + 0 = 0 + -6y x = 0 + -6y Remove the zero: x = -6y Simplifying x = -6ySolution
x = {5y, -6y}
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