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Simplifying x4 + px3 + qx2 + -2x3 + -2px2 + -2qx + x3 + px2 + qx2 + qx + -2x2 = 0 Reorder the terms: -2px2 + px2 + px3 + -2qx + qx + qx2 + qx2 + -2x2 + -2x3 + x3 + x4 = 0 Combine like terms: -2px2 + px2 = -1px2 -1px2 + px3 + -2qx + qx + qx2 + qx2 + -2x2 + -2x3 + x3 + x4 = 0 Combine like terms: -2qx + qx = -1qx -1px2 + px3 + -1qx + qx2 + qx2 + -2x2 + -2x3 + x3 + x4 = 0 Combine like terms: qx2 + qx2 = 2qx2 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -2x3 + x3 + x4 = 0 Combine like terms: -2x3 + x3 = -1x3 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = 0 Solving -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add 'qx' to each side of the equation. -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + qx + x4 = 0 + qx Reorder the terms: -1px2 + px3 + -1qx + qx + 2qx2 + -2x2 + -1x3 + x4 = 0 + qx Combine like terms: -1qx + qx = 0 -1px2 + px3 + 0 + 2qx2 + -2x2 + -1x3 + x4 = 0 + qx -1px2 + px3 + 2qx2 + -2x2 + -1x3 + x4 = 0 + qx Remove the zero: -1px2 + px3 + 2qx2 + -2x2 + -1x3 + x4 = qx Add '-2qx2' to each side of the equation. -1px2 + px3 + 2qx2 + -2x2 + -1x3 + -2qx2 + x4 = qx + -2qx2 Reorder the terms: -1px2 + px3 + 2qx2 + -2qx2 + -2x2 + -1x3 + x4 = qx + -2qx2 Combine like terms: 2qx2 + -2qx2 = 0 -1px2 + px3 + 0 + -2x2 + -1x3 + x4 = qx + -2qx2 -1px2 + px3 + -2x2 + -1x3 + x4 = qx + -2qx2 Add '2x2' to each side of the equation. -1px2 + px3 + -2x2 + -1x3 + 2x2 + x4 = qx + -2qx2 + 2x2 Reorder the terms: -1px2 + px3 + -2x2 + 2x2 + -1x3 + x4 = qx + -2qx2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -1px2 + px3 + 0 + -1x3 + x4 = qx + -2qx2 + 2x2 -1px2 + px3 + -1x3 + x4 = qx + -2qx2 + 2x2 Add 'x3' to each side of the equation. -1px2 + px3 + -1x3 + x3 + x4 = qx + -2qx2 + 2x2 + x3 Combine like terms: -1x3 + x3 = 0 -1px2 + px3 + 0 + x4 = qx + -2qx2 + 2x2 + x3 -1px2 + px3 + x4 = qx + -2qx2 + 2x2 + x3 Add '-1x4' to each side of the equation. -1px2 + px3 + x4 + -1x4 = qx + -2qx2 + 2x2 + x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -1px2 + px3 + 0 = qx + -2qx2 + 2x2 + x3 + -1x4 -1px2 + px3 = qx + -2qx2 + 2x2 + x3 + -1x4 Reorder the terms: -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = qx + -1qx + -2qx2 + 2qx2 + 2x2 + -2x2 + x3 + -1x3 + -1x4 + x4 Combine like terms: qx + -1qx = 0 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = 0 + -2qx2 + 2qx2 + 2x2 + -2x2 + x3 + -1x3 + -1x4 + x4 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = -2qx2 + 2qx2 + 2x2 + -2x2 + x3 + -1x3 + -1x4 + x4 Combine like terms: -2qx2 + 2qx2 = 0 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = 0 + 2x2 + -2x2 + x3 + -1x3 + -1x4 + x4 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = 2x2 + -2x2 + x3 + -1x3 + -1x4 + x4 Combine like terms: 2x2 + -2x2 = 0 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = 0 + x3 + -1x3 + -1x4 + x4 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = x3 + -1x3 + -1x4 + x4 Combine like terms: x3 + -1x3 = 0 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = 0 + -1x4 + x4 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -1px2 + px3 + -1qx + 2qx2 + -2x2 + -1x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1px + px2 + -1q + 2qx + -2x + -1x2 + x3) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing p to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1px + px2 + -1q + 2qx + -2x + -1x2 + x3)' equal to zero and attempt to solve: Simplifying -1px + px2 + -1q + 2qx + -2x + -1x2 + x3 = 0 Solving -1px + px2 + -1q + 2qx + -2x + -1x2 + x3 = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. -1px + px2 + -1q + 2qx + -2x + -1x2 + q + x3 = 0 + q Reorder the terms: -1px + px2 + -1q + q + 2qx + -2x + -1x2 + x3 = 0 + q Combine like terms: -1q + q = 0 -1px + px2 + 0 + 2qx + -2x + -1x2 + x3 = 0 + q -1px + px2 + 2qx + -2x + -1x2 + x3 = 0 + q Remove the zero: -1px + px2 + 2qx + -2x + -1x2 + x3 = q Add '-2qx' to each side of the equation. -1px + px2 + 2qx + -2x + -1x2 + -2qx + x3 = q + -2qx Reorder the terms: -1px + px2 + 2qx + -2qx + -2x + -1x2 + x3 = q + -2qx Combine like terms: 2qx + -2qx = 0 -1px + px2 + 0 + -2x + -1x2 + x3 = q + -2qx -1px + px2 + -2x + -1x2 + x3 = q + -2qx Add '2x' to each side of the equation. -1px + px2 + -2x + -1x2 + 2x + x3 = q + -2qx + 2x Reorder the terms: -1px + px2 + -2x + 2x + -1x2 + x3 = q + -2qx + 2x Combine like terms: -2x + 2x = 0 -1px + px2 + 0 + -1x2 + x3 = q + -2qx + 2x -1px + px2 + -1x2 + x3 = q + -2qx + 2x Add 'x2' to each side of the equation. -1px + px2 + -1x2 + x2 + x3 = q + -2qx + 2x + x2 Combine like terms: -1x2 + x2 = 0 -1px + px2 + 0 + x3 = q + -2qx + 2x + x2 -1px + px2 + x3 = q + -2qx + 2x + x2 Add '-1x3' to each side of the equation. -1px + px2 + x3 + -1x3 = q + -2qx + 2x + x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -1px + px2 + 0 = q + -2qx + 2x + x2 + -1x3 -1px + px2 = q + -2qx + 2x + x2 + -1x3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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