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