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Simplifying (x + -1p)(2x2 + -1qx + 2) = 2x3 + -11x2 + 17x + -6 Reorder the terms: (-1p + x)(2x2 + -1qx + 2) = 2x3 + -11x2 + 17x + -6 Reorder the terms: (-1p + x)(2 + -1qx + 2x2) = 2x3 + -11x2 + 17x + -6 Multiply (-1p + x) * (2 + -1qx + 2x2) (-1p * (2 + -1qx + 2x2) + x(2 + -1qx + 2x2)) = 2x3 + -11x2 + 17x + -6 ((2 * -1p + -1qx * -1p + 2x2 * -1p) + x(2 + -1qx + 2x2)) = 2x3 + -11x2 + 17x + -6 ((-2p + 1pqx + -2px2) + x(2 + -1qx + 2x2)) = 2x3 + -11x2 + 17x + -6 (-2p + 1pqx + -2px2 + (2 * x + -1qx * x + 2x2 * x)) = 2x3 + -11x2 + 17x + -6 Reorder the terms: (-2p + 1pqx + -2px2 + (-1qx2 + 2x + 2x3)) = 2x3 + -11x2 + 17x + -6 (-2p + 1pqx + -2px2 + (-1qx2 + 2x + 2x3)) = 2x3 + -11x2 + 17x + -6 (-2p + 1pqx + -2px2 + -1qx2 + 2x + 2x3) = 2x3 + -11x2 + 17x + -6 Reorder the terms: -2p + 1pqx + -2px2 + -1qx2 + 2x + 2x3 = -6 + 17x + -11x2 + 2x3 Add '-2x3' to each side of the equation. -2p + 1pqx + -2px2 + -1qx2 + 2x + 2x3 + -2x3 = -6 + 17x + -11x2 + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -2p + 1pqx + -2px2 + -1qx2 + 2x + 0 = -6 + 17x + -11x2 + 2x3 + -2x3 -2p + 1pqx + -2px2 + -1qx2 + 2x = -6 + 17x + -11x2 + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -2p + 1pqx + -2px2 + -1qx2 + 2x = -6 + 17x + -11x2 + 0 -2p + 1pqx + -2px2 + -1qx2 + 2x = -6 + 17x + -11x2 Solving -2p + 1pqx + -2px2 + -1qx2 + 2x = -6 + 17x + -11x2 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add 'qx2' to each side of the equation. -2p + 1pqx + -2px2 + -1qx2 + qx2 + 2x = -6 + 17x + qx2 + -11x2 Combine like terms: -1qx2 + qx2 = 0 -2p + 1pqx + -2px2 + 0 + 2x = -6 + 17x + qx2 + -11x2 -2p + 1pqx + -2px2 + 2x = -6 + 17x + qx2 + -11x2 Reorder the terms: -2p + 1pqx + -2px2 + 2x = -6 + qx2 + 17x + -11x2 Add '-2x' to each side of the equation. -2p + 1pqx + -2px2 + 2x + -2x = -6 + qx2 + 17x + -2x + -11x2 Combine like terms: 2x + -2x = 0 -2p + 1pqx + -2px2 + 0 = -6 + qx2 + 17x + -2x + -11x2 -2p + 1pqx + -2px2 = -6 + qx2 + 17x + -2x + -11x2 Combine like terms: 17x + -2x = 15x -2p + 1pqx + -2px2 = -6 + qx2 + 15x + -11x2 Reorder the terms: 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = -6 + qx2 + 15x + -11x2 + 6 + -1qx2 + -15x + 11x2 Reorder the terms: 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = -6 + 6 + qx2 + -1qx2 + 15x + -15x + -11x2 + 11x2 Combine like terms: -6 + 6 = 0 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = 0 + qx2 + -1qx2 + 15x + -15x + -11x2 + 11x2 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = qx2 + -1qx2 + 15x + -15x + -11x2 + 11x2 Combine like terms: qx2 + -1qx2 = 0 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = 0 + 15x + -15x + -11x2 + 11x2 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = 15x + -15x + -11x2 + 11x2 Combine like terms: 15x + -15x = 0 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = 0 + -11x2 + 11x2 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = -11x2 + 11x2 Combine like terms: -11x2 + 11x2 = 0 6 + -2p + 1pqx + -2px2 + -1qx2 + -15x + 11x2 = 0 The solution to this equation could not be determined.
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