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Simplifying x2 + -5y2 = 4 Solving x2 + -5y2 = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5y2' to each side of the equation. x2 + -5y2 + 5y2 = 4 + 5y2 Combine like terms: -5y2 + 5y2 = 0 x2 + 0 = 4 + 5y2 x2 = 4 + 5y2 Simplifying x2 = 4 + 5y2 Reorder the terms: -4 + x2 + -5y2 = 4 + 5y2 + -4 + -5y2 Reorder the terms: -4 + x2 + -5y2 = 4 + -4 + 5y2 + -5y2 Combine like terms: 4 + -4 = 0 -4 + x2 + -5y2 = 0 + 5y2 + -5y2 -4 + x2 + -5y2 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 -4 + x2 + -5y2 = 0 Factor a trinomial. (x + -5y)(x + y) = 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 + 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 = {5y, -1y}
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