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Simplifying x2 + -8y2 = 7 Solving x2 + -8y2 = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8y2' to each side of the equation. x2 + -8y2 + 8y2 = 7 + 8y2 Combine like terms: -8y2 + 8y2 = 0 x2 + 0 = 7 + 8y2 x2 = 7 + 8y2 Simplifying x2 = 7 + 8y2 Reorder the terms: -7 + x2 + -8y2 = 7 + 8y2 + -7 + -8y2 Reorder the terms: -7 + x2 + -8y2 = 7 + -7 + 8y2 + -8y2 Combine like terms: 7 + -7 = 0 -7 + x2 + -8y2 = 0 + 8y2 + -8y2 -7 + x2 + -8y2 = 8y2 + -8y2 Combine like terms: 8y2 + -8y2 = 0 -7 + x2 + -8y2 = 0 Factor a trinomial. (x + -8y)(x + y) = 0Subproblem 1
Set the factor '(x + -8y)' equal to zero and attempt to solve: Simplifying x + -8y = 0 Solving x + -8y = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. x + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 x + 0 = 0 + 8y x = 0 + 8y Remove the zero: x = 8y Simplifying x = 8ySubproblem 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 = {8y, -1y}
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