x^2+3y^2=4

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Solution for x^2+3y^2=4 equation:


Simplifying
x2 + 3y2 = 4

Solving
x2 + 3y2 = 4

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.
x2 + 3y2 + -3y2 = 4 + -3y2

Combine like terms: 3y2 + -3y2 = 0
x2 + 0 = 4 + -3y2
x2 = 4 + -3y2

Simplifying
x2 = 4 + -3y2

Reorder the terms:
-4 + x2 + 3y2 = 4 + -3y2 + -4 + 3y2

Reorder the terms:
-4 + x2 + 3y2 = 4 + -4 + -3y2 + 3y2

Combine like terms: 4 + -4 = 0
-4 + x2 + 3y2 = 0 + -3y2 + 3y2
-4 + x2 + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
-4 + x2 + 3y2 = 0

Factor a trinomial.
(x + -3y)(x + -1y) = 0

Subproblem 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 = 3y

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 = {3y, y}

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