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Simplifying [p + -1(q + r)][p + q + r] = 0 [p + (q * -1 + r * -1)][p + q + r] = 0 [p + (-1q + -1r)][p + q + r] = 0 Multiply [p + -1q + -1r] * [p + q + r] [p[p + q + r] + -1q * [p + q + r] + -1r * [p + q + r]] = 0 [[p * p + q * p + r * p] + -1q * [p + q + r] + -1r * [p + q + r]] = 0 Reorder the terms: [[pq + pr + p2] + -1q * [p + q + r] + -1r * [p + q + r]] = 0 [[pq + pr + p2] + -1q * [p + q + r] + -1r * [p + q + r]] = 0 [pq + pr + p2 + [p * -1q + q * -1q + r * -1q] + -1r * [p + q + r]] = 0 Reorder the terms: [pq + pr + p2 + [-1pq + -1qr + -1q2] + -1r * [p + q + r]] = 0 [pq + pr + p2 + [-1pq + -1qr + -1q2] + -1r * [p + q + r]] = 0 [pq + pr + p2 + -1pq + -1qr + -1q2 + [p * -1r + q * -1r + r * -1r]] = 0 [pq + pr + p2 + -1pq + -1qr + -1q2 + [-1pr + -1qr + -1r2]] = 0 Reorder the terms: [pq + -1pq + pr + -1pr + p2 + -1qr + -1qr + -1q2 + -1r2] = 0 Combine like terms: pq + -1pq = 0 [0 + pr + -1pr + p2 + -1qr + -1qr + -1q2 + -1r2] = 0 [pr + -1pr + p2 + -1qr + -1qr + -1q2 + -1r2] = 0 Combine like terms: pr + -1pr = 0 [0 + p2 + -1qr + -1qr + -1q2 + -1r2] = 0 [p2 + -1qr + -1qr + -1q2 + -1r2] = 0 Combine like terms: -1qr + -1qr = -2qr [p2 + -2qr + -1q2 + -1r2] = 0 Solving p2 + -2qr + -1q2 + -1r2 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2qr' to each side of the equation. p2 + -2qr + -1q2 + 2qr + -1r2 = 0 + 2qr Reorder the terms: p2 + -2qr + 2qr + -1q2 + -1r2 = 0 + 2qr Combine like terms: -2qr + 2qr = 0 p2 + 0 + -1q2 + -1r2 = 0 + 2qr p2 + -1q2 + -1r2 = 0 + 2qr Remove the zero: p2 + -1q2 + -1r2 = 2qr Add 'q2' to each side of the equation. p2 + -1q2 + q2 + -1r2 = 2qr + q2 Combine like terms: -1q2 + q2 = 0 p2 + 0 + -1r2 = 2qr + q2 p2 + -1r2 = 2qr + q2 Add 'r2' to each side of the equation. p2 + -1r2 + r2 = 2qr + q2 + r2 Combine like terms: -1r2 + r2 = 0 p2 + 0 = 2qr + q2 + r2 p2 = 2qr + q2 + r2 Simplifying p2 = 2qr + q2 + r2 Reorder the terms: p2 + -2qr + -1q2 + -1r2 = 2qr + -2qr + q2 + -1q2 + r2 + -1r2 Combine like terms: 2qr + -2qr = 0 p2 + -2qr + -1q2 + -1r2 = 0 + q2 + -1q2 + r2 + -1r2 p2 + -2qr + -1q2 + -1r2 = q2 + -1q2 + r2 + -1r2 Combine like terms: q2 + -1q2 = 0 p2 + -2qr + -1q2 + -1r2 = 0 + r2 + -1r2 p2 + -2qr + -1q2 + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 p2 + -2qr + -1q2 + -1r2 = 0 The solution to this equation could not be determined.
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