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Simplifying 4x2 + 16y2 = 16 Solving 4x2 + 16y2 = 16 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16y2' to each side of the equation. 4x2 + 16y2 + -16y2 = 16 + -16y2 Combine like terms: 16y2 + -16y2 = 0 4x2 + 0 = 16 + -16y2 4x2 = 16 + -16y2 Divide each side by '4'. x2 = 4 + -4y2 Simplifying x2 = 4 + -4y2 Reorder the terms: -4 + x2 + 4y2 = 4 + -4y2 + -4 + 4y2 Reorder the terms: -4 + x2 + 4y2 = 4 + -4 + -4y2 + 4y2 Combine like terms: 4 + -4 = 0 -4 + x2 + 4y2 = 0 + -4y2 + 4y2 -4 + x2 + 4y2 = -4y2 + 4y2 Combine like terms: -4y2 + 4y2 = 0 -4 + x2 + 4y2 = 0 Factor a trinomial. (x + -2y)(x + -2y) = 0Subproblem 1
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySubproblem 2
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySolution
x = {2y, 2y}
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