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Simplifying
4x2 + -3xy + 5y2 + 10xy + -17y2 + -11x2 + -5xy + 12x2 + -2xy = 0
Reorder the terms:
-3xy + 10xy + -5xy + -2xy + 4x2 + -11x2 + 12x2 + 5y2 + -17y2 = 0
Combine like terms: -3xy + 10xy = 7xy
7xy + -5xy + -2xy + 4x2 + -11x2 + 12x2 + 5y2 + -17y2 = 0
Combine like terms: 7xy + -5xy = 2xy
2xy + -2xy + 4x2 + -11x2 + 12x2 + 5y2 + -17y2 = 0
Combine like terms: 2xy + -2xy = 0
0 + 4x2 + -11x2 + 12x2 + 5y2 + -17y2 = 0
4x2 + -11x2 + 12x2 + 5y2 + -17y2 = 0
Combine like terms: 4x2 + -11x2 = -7x2
-7x2 + 12x2 + 5y2 + -17y2 = 0
Combine like terms: -7x2 + 12x2 = 5x2
5x2 + 5y2 + -17y2 = 0
Combine like terms: 5y2 + -17y2 = -12y2
5x2 + -12y2 = 0
Solving
5x2 + -12y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '12y2' to each side of the equation.
5x2 + -12y2 + 12y2 = 0 + 12y2
Combine like terms: -12y2 + 12y2 = 0
5x2 + 0 = 0 + 12y2
5x2 = 0 + 12y2
Remove the zero:
5x2 = 12y2
Divide each side by '5'.
x2 = 2.4y2
Simplifying
x2 = 2.4y2
Take the square root of each side:
x = {-1.549193338y, 1.549193338y}
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