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Simplifying ax4 + bx3 + cx2 + dx + e = 0 Solving ax4 + bx3 + cx2 + dx + e = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx3' to each side of the equation. ax4 + bx3 + cx2 + dx + -1bx3 + e = 0 + -1bx3 Reorder the terms: ax4 + bx3 + -1bx3 + cx2 + dx + e = 0 + -1bx3 Combine like terms: bx3 + -1bx3 = 0 ax4 + 0 + cx2 + dx + e = 0 + -1bx3 ax4 + cx2 + dx + e = 0 + -1bx3 Remove the zero: ax4 + cx2 + dx + e = -1bx3 Add '-1cx2' to each side of the equation. ax4 + cx2 + dx + -1cx2 + e = -1bx3 + -1cx2 Reorder the terms: ax4 + cx2 + -1cx2 + dx + e = -1bx3 + -1cx2 Combine like terms: cx2 + -1cx2 = 0 ax4 + 0 + dx + e = -1bx3 + -1cx2 ax4 + dx + e = -1bx3 + -1cx2 Add '-1dx' to each side of the equation. ax4 + dx + -1dx + e = -1bx3 + -1cx2 + -1dx Combine like terms: dx + -1dx = 0 ax4 + 0 + e = -1bx3 + -1cx2 + -1dx ax4 + e = -1bx3 + -1cx2 + -1dx Add '-1e' to each side of the equation. ax4 + e + -1e = -1bx3 + -1cx2 + -1dx + -1e Combine like terms: e + -1e = 0 ax4 + 0 = -1bx3 + -1cx2 + -1dx + -1e ax4 = -1bx3 + -1cx2 + -1dx + -1e Divide each side by 'x4'. a = -1bx-1 + -1cx-2 + -1dx-3 + -1ex-4 Simplifying a = -1bx-1 + -1cx-2 + -1dx-3 + -1ex-4
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