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Simplifying 4x2 + 4y2 = 8 Solving 4x2 + 4y2 = 8 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. 4x2 + 4y2 + -4y2 = 8 + -4y2 Combine like terms: 4y2 + -4y2 = 0 4x2 + 0 = 8 + -4y2 4x2 = 8 + -4y2 Divide each side by '4'. x2 = 2 + -1y2 Simplifying x2 = 2 + -1y2 Reorder the terms: -2 + x2 + y2 = 2 + -1y2 + -2 + y2 Reorder the terms: -2 + x2 + y2 = 2 + -2 + -1y2 + y2 Combine like terms: 2 + -2 = 0 -2 + x2 + y2 = 0 + -1y2 + y2 -2 + x2 + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -2 + x2 + y2 = 0 Factor a trinomial. (x + -1y)(x + -1y) = 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 + -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 = {y, y}
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