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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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