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Simplifying x2 + 4y2 = 5 Solving x2 + 4y2 = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4y2' to each side of the equation. x2 + 4y2 + -4y2 = 5 + -4y2 Combine like terms: 4y2 + -4y2 = 0 x2 + 0 = 5 + -4y2 x2 = 5 + -4y2 Simplifying x2 = 5 + -4y2 Reorder the terms: -5 + x2 + 4y2 = 5 + -4y2 + -5 + 4y2 Reorder the terms: -5 + x2 + 4y2 = 5 + -5 + -4y2 + 4y2 Combine like terms: 5 + -5 = 0 -5 + x2 + 4y2 = 0 + -4y2 + 4y2 -5 + x2 + 4y2 = -4y2 + 4y2 Combine like terms: -4y2 + 4y2 = 0 -5 + x2 + 4y2 = 0 Factor a trinomial. (x + -4y)(x + -1y) = 0Subproblem 1
Set the factor '(x + -4y)' equal to zero and attempt to solve: Simplifying x + -4y = 0 Solving x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 x + 0 = 0 + 4y x = 0 + 4y Remove the zero: x = 4y Simplifying x = 4ySubproblem 2
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 = ySolution
x = {4y, y}
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