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