x^2+5y^2=6

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Solution for x^2+5y^2=6 equation:


Simplifying
x2 + 5y2 = 6

Solving
x2 + 5y2 = 6

Solving for variable 'x'.

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

Add '-5y2' to each side of the equation.
x2 + 5y2 + -5y2 = 6 + -5y2

Combine like terms: 5y2 + -5y2 = 0
x2 + 0 = 6 + -5y2
x2 = 6 + -5y2

Simplifying
x2 = 6 + -5y2

Reorder the terms:
-6 + x2 + 5y2 = 6 + -5y2 + -6 + 5y2

Reorder the terms:
-6 + x2 + 5y2 = 6 + -6 + -5y2 + 5y2

Combine like terms: 6 + -6 = 0
-6 + x2 + 5y2 = 0 + -5y2 + 5y2
-6 + x2 + 5y2 = -5y2 + 5y2

Combine like terms: -5y2 + 5y2 = 0
-6 + x2 + 5y2 = 0

Factor a trinomial.
(x + -5y)(x + -1y) = 0

Subproblem 1

Set the factor '(x + -5y)' equal to zero and attempt to solve: Simplifying x + -5y = 0 Solving x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 x + 0 = 0 + 5y x = 0 + 5y Remove the zero: x = 5y Simplifying x = 5y

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 = {5y, y}

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