3x^2+3y^2=6

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Solution for 3x^2+3y^2=6 equation:


Simplifying
3x2 + 3y2 = 6

Solving
3x2 + 3y2 = 6

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3y2' to each side of the equation.
3x2 + 3y2 + -3y2 = 6 + -3y2

Combine like terms: 3y2 + -3y2 = 0
3x2 + 0 = 6 + -3y2
3x2 = 6 + -3y2

Divide each side by '3'.
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) = 0

Subproblem 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 = y

Subproblem 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 = y

Solution

x = {y, y}

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