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Simplifying 2x2 + 12 + 18y2 = 0 Reorder the terms: 12 + 2x2 + 18y2 = 0 Solving 12 + 2x2 + 18y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 2x2 + -12 + 18y2 = 0 + -12 Reorder the terms: 12 + -12 + 2x2 + 18y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 2x2 + 18y2 = 0 + -12 2x2 + 18y2 = 0 + -12 Combine like terms: 0 + -12 = -12 2x2 + 18y2 = -12 Add '-18y2' to each side of the equation. 2x2 + 18y2 + -18y2 = -12 + -18y2 Combine like terms: 18y2 + -18y2 = 0 2x2 + 0 = -12 + -18y2 2x2 = -12 + -18y2 Divide each side by '2'. x2 = -6 + -9y2 Simplifying x2 = -6 + -9y2 Reorder the terms: 6 + x2 + 9y2 = -6 + -9y2 + 6 + 9y2 Reorder the terms: 6 + x2 + 9y2 = -6 + 6 + -9y2 + 9y2 Combine like terms: -6 + 6 = 0 6 + x2 + 9y2 = 0 + -9y2 + 9y2 6 + x2 + 9y2 = -9y2 + 9y2 Combine like terms: -9y2 + 9y2 = 0 6 + x2 + 9y2 = 0 Factor a trinomial. (x + 3y)(x + 3y) = 0Subproblem 1
Set the factor '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySubproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySolution
x = {-3y, -3y}
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