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Simplifying sqrt(x + -2sqrt(x + -1)) = 2sqrt(2sqrt(-1 + x) + x) Reorder the terms: qrst(x + -2qrst(-1 + x)) = 2sqrt(2sqrt(-1 + x) + x) qrst(x + (-1 * -2qrst + x * -2qrst)) = 2sqrt(2sqrt(-1 + x) + x) qrst(x + (2qrst + -2qrstx)) = 2sqrt(2sqrt(-1 + x) + x) Reorder the terms: qrst(2qrst + -2qrstx + x) = 2sqrt(2sqrt(-1 + x) + x) (2qrst * qrst + -2qrstx * qrst + x * qrst) = 2sqrt(2sqrt(-1 + x) + x) Reorder the terms: (qrstx + 2q2r2s2t2 + -2q2r2s2t2x) = 2sqrt(2sqrt(-1 + x) + x) (qrstx + 2q2r2s2t2 + -2q2r2s2t2x) = 2sqrt(2sqrt(-1 + x) + x) qrstx + 2q2r2s2t2 + -2q2r2s2t2x = 2qrst((-1 * 2qrst + x * 2qrst) + x) qrstx + 2q2r2s2t2 + -2q2r2s2t2x = 2qrst((-2qrst + 2qrstx) + x) qrstx + 2q2r2s2t2 + -2q2r2s2t2x = (-2qrst * 2qrst + 2qrstx * 2qrst + x * 2qrst) Reorder the terms: qrstx + 2q2r2s2t2 + -2q2r2s2t2x = (2qrstx + -4q2r2s2t2 + 4q2r2s2t2x) qrstx + 2q2r2s2t2 + -2q2r2s2t2x = (2qrstx + -4q2r2s2t2 + 4q2r2s2t2x) Solving qrstx + 2q2r2s2t2 + -2q2r2s2t2x = 2qrstx + -4q2r2s2t2 + 4q2r2s2t2x Solving for variable 'q'. Reorder the terms: qrstx + -2qrstx + 2q2r2s2t2 + 4q2r2s2t2 + -2q2r2s2t2x + -4q2r2s2t2x = 2qrstx + -4q2r2s2t2 + 4q2r2s2t2x + -2qrstx + 4q2r2s2t2 + -4q2r2s2t2x Combine like terms: qrstx + -2qrstx = -1qrstx -1qrstx + 2q2r2s2t2 + 4q2r2s2t2 + -2q2r2s2t2x + -4q2r2s2t2x = 2qrstx + -4q2r2s2t2 + 4q2r2s2t2x + -2qrstx + 4q2r2s2t2 + -4q2r2s2t2x Combine like terms: 2q2r2s2t2 + 4q2r2s2t2 = 6q2r2s2t2 -1qrstx + 6q2r2s2t2 + -2q2r2s2t2x + -4q2r2s2t2x = 2qrstx + -4q2r2s2t2 + 4q2r2s2t2x + -2qrstx + 4q2r2s2t2 + -4q2r2s2t2x Combine like terms: -2q2r2s2t2x + -4q2r2s2t2x = -6q2r2s2t2x -1qrstx + 6q2r2s2t2 + -6q2r2s2t2x = 2qrstx + -4q2r2s2t2 + 4q2r2s2t2x + -2qrstx + 4q2r2s2t2 + -4q2r2s2t2x Reorder the terms: -1qrstx + 6q2r2s2t2 + -6q2r2s2t2x = 2qrstx + -2qrstx + -4q2r2s2t2 + 4q2r2s2t2 + 4q2r2s2t2x + -4q2r2s2t2x Combine like terms: 2qrstx + -2qrstx = 0 -1qrstx + 6q2r2s2t2 + -6q2r2s2t2x = 0 + -4q2r2s2t2 + 4q2r2s2t2 + 4q2r2s2t2x + -4q2r2s2t2x -1qrstx + 6q2r2s2t2 + -6q2r2s2t2x = -4q2r2s2t2 + 4q2r2s2t2 + 4q2r2s2t2x + -4q2r2s2t2x Combine like terms: -4q2r2s2t2 + 4q2r2s2t2 = 0 -1qrstx + 6q2r2s2t2 + -6q2r2s2t2x = 0 + 4q2r2s2t2x + -4q2r2s2t2x -1qrstx + 6q2r2s2t2 + -6q2r2s2t2x = 4q2r2s2t2x + -4q2r2s2t2x Combine like terms: 4q2r2s2t2x + -4q2r2s2t2x = 0 -1qrstx + 6q2r2s2t2 + -6q2r2s2t2x = 0 Factor out the Greatest Common Factor (GCF), 'qrst'. qrst(-1x + 6qrst + -6qrstx) = 0Subproblem 1
Set the factor 'qrst' equal to zero and attempt to solve: Simplifying qrst = 0 Solving qrst = 0 Move all terms containing q to the left, all other terms to the right. Simplifying qrst = 0 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 '(-1x + 6qrst + -6qrstx)' equal to zero and attempt to solve: Simplifying -1x + 6qrst + -6qrstx = 0 Reorder the terms: 6qrst + -6qrstx + -1x = 0 Solving 6qrst + -6qrstx + -1x = 0 Move all terms containing q to the left, all other terms to the right. Add 'x' to each side of the equation. 6qrst + -6qrstx + -1x + x = 0 + x Combine like terms: -1x + x = 0 6qrst + -6qrstx + 0 = 0 + x 6qrst + -6qrstx = 0 + x Remove the zero: 6qrst + -6qrstx = x 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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