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Simplifying x2 + -6y + -7y2 = 0 Solving x2 + -6y + -7y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6y' to each side of the equation. x2 + -6y + 6y + -7y2 = 0 + 6y Combine like terms: -6y + 6y = 0 x2 + 0 + -7y2 = 0 + 6y x2 + -7y2 = 0 + 6y Remove the zero: x2 + -7y2 = 6y Add '7y2' to each side of the equation. x2 + -7y2 + 7y2 = 6y + 7y2 Combine like terms: -7y2 + 7y2 = 0 x2 + 0 = 6y + 7y2 x2 = 6y + 7y2 Simplifying x2 = 6y + 7y2 Reorder the terms: x2 + -6y + -7y2 = 6y + -6y + 7y2 + -7y2 Combine like terms: 6y + -6y = 0 x2 + -6y + -7y2 = 0 + 7y2 + -7y2 x2 + -6y + -7y2 = 7y2 + -7y2 Combine like terms: 7y2 + -7y2 = 0 x2 + -6y + -7y2 = 0 Factor a trinomial. (x + -7y)(x + y) = 0Subproblem 1
Set the factor '(x + -7y)' equal to zero and attempt to solve: Simplifying x + -7y = 0 Solving x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 x + 0 = 0 + 7y x = 0 + 7y Remove the zero: x = 7y Simplifying x = 7ySubproblem 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 = {7y, -1y}
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