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Simplifying x4 + px3 + qx2 + rx + s = 0 Reorder the terms: px3 + qx2 + rx + s + x4 = 0 Solving px3 + qx2 + rx + s + x4 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1qx2' to each side of the equation. px3 + qx2 + rx + s + -1qx2 + x4 = 0 + -1qx2 Reorder the terms: px3 + qx2 + -1qx2 + rx + s + x4 = 0 + -1qx2 Combine like terms: qx2 + -1qx2 = 0 px3 + 0 + rx + s + x4 = 0 + -1qx2 px3 + rx + s + x4 = 0 + -1qx2 Remove the zero: px3 + rx + s + x4 = -1qx2 Add '-1rx' to each side of the equation. px3 + rx + s + -1rx + x4 = -1qx2 + -1rx Reorder the terms: px3 + rx + -1rx + s + x4 = -1qx2 + -1rx Combine like terms: rx + -1rx = 0 px3 + 0 + s + x4 = -1qx2 + -1rx px3 + s + x4 = -1qx2 + -1rx Add '-1s' to each side of the equation. px3 + s + -1s + x4 = -1qx2 + -1rx + -1s Combine like terms: s + -1s = 0 px3 + 0 + x4 = -1qx2 + -1rx + -1s px3 + x4 = -1qx2 + -1rx + -1s Add '-1x4' to each side of the equation. px3 + x4 + -1x4 = -1qx2 + -1rx + -1s + -1x4 Combine like terms: x4 + -1x4 = 0 px3 + 0 = -1qx2 + -1rx + -1s + -1x4 px3 = -1qx2 + -1rx + -1s + -1x4 Divide each side by 'x3'. p = -1qx-1 + -1rx-2 + -1sx-3 + -1x Simplifying p = -1qx-1 + -1rx-2 + -1sx-3 + -1x
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