ax^2+by^2+cxy+dx+ey=0

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Solution for ax^2+by^2+cxy+dx+ey=0 equation:


Simplifying
ax2 + by2 + cxy + dx + ey = 0

Solving
ax2 + by2 + cxy + dx + ey = 0

Solving for variable 'a'.

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

Add '-1by2' to each side of the equation.
ax2 + by2 + cxy + dx + -1by2 + ey = 0 + -1by2

Reorder the terms:
ax2 + by2 + -1by2 + cxy + dx + ey = 0 + -1by2

Combine like terms: by2 + -1by2 = 0
ax2 + 0 + cxy + dx + ey = 0 + -1by2
ax2 + cxy + dx + ey = 0 + -1by2
Remove the zero:
ax2 + cxy + dx + ey = -1by2

Add '-1cxy' to each side of the equation.
ax2 + cxy + dx + -1cxy + ey = -1by2 + -1cxy

Reorder the terms:
ax2 + cxy + -1cxy + dx + ey = -1by2 + -1cxy

Combine like terms: cxy + -1cxy = 0
ax2 + 0 + dx + ey = -1by2 + -1cxy
ax2 + dx + ey = -1by2 + -1cxy

Add '-1dx' to each side of the equation.
ax2 + dx + -1dx + ey = -1by2 + -1cxy + -1dx

Combine like terms: dx + -1dx = 0
ax2 + 0 + ey = -1by2 + -1cxy + -1dx
ax2 + ey = -1by2 + -1cxy + -1dx

Add '-1ey' to each side of the equation.
ax2 + ey + -1ey = -1by2 + -1cxy + -1dx + -1ey

Combine like terms: ey + -1ey = 0
ax2 + 0 = -1by2 + -1cxy + -1dx + -1ey
ax2 = -1by2 + -1cxy + -1dx + -1ey

Divide each side by 'x2'.
a = -1bx-2y2 + -1cx-1y + -1dx-1 + -1ex-2y

Simplifying
a = -1bx-2y2 + -1cx-1y + -1dx-1 + -1ex-2y

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