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Simplifying x2 + -10y2 = 9 Solving x2 + -10y2 = 9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10y2' to each side of the equation. x2 + -10y2 + 10y2 = 9 + 10y2 Combine like terms: -10y2 + 10y2 = 0 x2 + 0 = 9 + 10y2 x2 = 9 + 10y2 Simplifying x2 = 9 + 10y2 Reorder the terms: -9 + x2 + -10y2 = 9 + 10y2 + -9 + -10y2 Reorder the terms: -9 + x2 + -10y2 = 9 + -9 + 10y2 + -10y2 Combine like terms: 9 + -9 = 0 -9 + x2 + -10y2 = 0 + 10y2 + -10y2 -9 + x2 + -10y2 = 10y2 + -10y2 Combine like terms: 10y2 + -10y2 = 0 -9 + x2 + -10y2 = 0 Factor a trinomial. (x + -10y)(x + y) = 0Subproblem 1
Set the factor '(x + -10y)' equal to zero and attempt to solve: Simplifying x + -10y = 0 Solving x + -10y = 0 Move all terms containing x to the left, all other terms to the right. Add '10y' to each side of the equation. x + -10y + 10y = 0 + 10y Combine like terms: -10y + 10y = 0 x + 0 = 0 + 10y x = 0 + 10y Remove the zero: x = 10y Simplifying x = 10ySubproblem 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 = {10y, -1y}
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