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Simplifying ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 Reorder the terms: ax2 + by2 + c + 2fy + 2gx + 2hxy = 0 Solving ax2 + by2 + c + 2fy + 2gx + 2hxy = 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 + c + 2fy + 2gx + -1by2 + 2hxy = 0 + -1by2 Reorder the terms: ax2 + by2 + -1by2 + c + 2fy + 2gx + 2hxy = 0 + -1by2 Combine like terms: by2 + -1by2 = 0 ax2 + 0 + c + 2fy + 2gx + 2hxy = 0 + -1by2 ax2 + c + 2fy + 2gx + 2hxy = 0 + -1by2 Remove the zero: ax2 + c + 2fy + 2gx + 2hxy = -1by2 Add '-1c' to each side of the equation. ax2 + c + 2fy + 2gx + -1c + 2hxy = -1by2 + -1c Reorder the terms: ax2 + c + -1c + 2fy + 2gx + 2hxy = -1by2 + -1c Combine like terms: c + -1c = 0 ax2 + 0 + 2fy + 2gx + 2hxy = -1by2 + -1c ax2 + 2fy + 2gx + 2hxy = -1by2 + -1c Add '-2fy' to each side of the equation. ax2 + 2fy + 2gx + -2fy + 2hxy = -1by2 + -1c + -2fy Reorder the terms: ax2 + 2fy + -2fy + 2gx + 2hxy = -1by2 + -1c + -2fy Combine like terms: 2fy + -2fy = 0 ax2 + 0 + 2gx + 2hxy = -1by2 + -1c + -2fy ax2 + 2gx + 2hxy = -1by2 + -1c + -2fy Add '-2gx' to each side of the equation. ax2 + 2gx + -2gx + 2hxy = -1by2 + -1c + -2fy + -2gx Combine like terms: 2gx + -2gx = 0 ax2 + 0 + 2hxy = -1by2 + -1c + -2fy + -2gx ax2 + 2hxy = -1by2 + -1c + -2fy + -2gx Add '-2hxy' to each side of the equation. ax2 + 2hxy + -2hxy = -1by2 + -1c + -2fy + -2gx + -2hxy Combine like terms: 2hxy + -2hxy = 0 ax2 + 0 = -1by2 + -1c + -2fy + -2gx + -2hxy ax2 = -1by2 + -1c + -2fy + -2gx + -2hxy Divide each side by 'x2'. a = -1bx-2y2 + -1cx-2 + -2fx-2y + -2gx-1 + -2hx-1y Simplifying a = -1bx-2y2 + -1cx-2 + -2fx-2y + -2gx-1 + -2hx-1y
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