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Simplifying
(7x2 + -2xy + 3y2) + -1(-3x2 + -2xy + 5y2) = 0
Reorder the terms:
(-2xy + 7x2 + 3y2) + -1(-3x2 + -2xy + 5y2) = 0
Remove parenthesis around (-2xy + 7x2 + 3y2)
-2xy + 7x2 + 3y2 + -1(-3x2 + -2xy + 5y2) = 0
Reorder the terms:
-2xy + 7x2 + 3y2 + -1(-2xy + -3x2 + 5y2) = 0
-2xy + 7x2 + 3y2 + (-2xy * -1 + -3x2 * -1 + 5y2 * -1) = 0
-2xy + 7x2 + 3y2 + (2xy + 3x2 + -5y2) = 0
Reorder the terms:
-2xy + 2xy + 7x2 + 3x2 + 3y2 + -5y2 = 0
Combine like terms: -2xy + 2xy = 0
0 + 7x2 + 3x2 + 3y2 + -5y2 = 0
7x2 + 3x2 + 3y2 + -5y2 = 0
Combine like terms: 7x2 + 3x2 = 10x2
10x2 + 3y2 + -5y2 = 0
Combine like terms: 3y2 + -5y2 = -2y2
10x2 + -2y2 = 0
Solving
10x2 + -2y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2y2' to each side of the equation.
10x2 + -2y2 + 2y2 = 0 + 2y2
Combine like terms: -2y2 + 2y2 = 0
10x2 + 0 = 0 + 2y2
10x2 = 0 + 2y2
Remove the zero:
10x2 = 2y2
Divide each side by '10'.
x2 = 0.2y2
Simplifying
x2 = 0.2y2
Take the square root of each side:
x = {-0.447213596y, 0.447213596y}
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