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Simplifying sqrt(2x + 2sqrt(2x + -1)) + -1sqrt(2x + -2sqrt(2x + -1)) = 2 Reorder the terms: qrst(2x + 2qrst(-1 + 2x)) + -1sqrt(2x + -2sqrt(2x + -1)) = 2 qrst(2x + (-1 * 2qrst + 2x * 2qrst)) + -1sqrt(2x + -2sqrt(2x + -1)) = 2 qrst(2x + (-2qrst + 4qrstx)) + -1sqrt(2x + -2sqrt(2x + -1)) = 2 Reorder the terms: qrst(-2qrst + 4qrstx + 2x) + -1sqrt(2x + -2sqrt(2x + -1)) = 2 (-2qrst * qrst + 4qrstx * qrst + 2x * qrst) + -1sqrt(2x + -2sqrt(2x + -1)) = 2 Reorder the terms: (2qrstx + -2q2r2s2t2 + 4q2r2s2t2x) + -1sqrt(2x + -2sqrt(2x + -1)) = 2 (2qrstx + -2q2r2s2t2 + 4q2r2s2t2x) + -1sqrt(2x + -2sqrt(2x + -1)) = 2 Reorder the terms: 2qrstx + -2q2r2s2t2 + 4q2r2s2t2x + -1qrst(2x + -2qrst(-1 + 2x)) = 2 2qrstx + -2q2r2s2t2 + 4q2r2s2t2x + -1qrst(2x + (-1 * -2qrst + 2x * -2qrst)) = 2 2qrstx + -2q2r2s2t2 + 4q2r2s2t2x + -1qrst(2x + (2qrst + -4qrstx)) = 2 Reorder the terms: 2qrstx + -2q2r2s2t2 + 4q2r2s2t2x + -1qrst(2qrst + -4qrstx + 2x) = 2 2qrstx + -2q2r2s2t2 + 4q2r2s2t2x + (2qrst * -1qrst + -4qrstx * -1qrst + 2x * -1qrst) = 2 Reorder the terms: 2qrstx + -2q2r2s2t2 + 4q2r2s2t2x + (-2qrstx + -2q2r2s2t2 + 4q2r2s2t2x) = 2 2qrstx + -2q2r2s2t2 + 4q2r2s2t2x + (-2qrstx + -2q2r2s2t2 + 4q2r2s2t2x) = 2 Reorder the terms: 2qrstx + -2qrstx + -2q2r2s2t2 + -2q2r2s2t2 + 4q2r2s2t2x + 4q2r2s2t2x = 2 Combine like terms: 2qrstx + -2qrstx = 0 0 + -2q2r2s2t2 + -2q2r2s2t2 + 4q2r2s2t2x + 4q2r2s2t2x = 2 -2q2r2s2t2 + -2q2r2s2t2 + 4q2r2s2t2x + 4q2r2s2t2x = 2 Combine like terms: -2q2r2s2t2 + -2q2r2s2t2 = -4q2r2s2t2 -4q2r2s2t2 + 4q2r2s2t2x + 4q2r2s2t2x = 2 Combine like terms: 4q2r2s2t2x + 4q2r2s2t2x = 8q2r2s2t2x -4q2r2s2t2 + 8q2r2s2t2x = 2 Solving -4q2r2s2t2 + 8q2r2s2t2x = 2 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Reorder the terms: -2 + -4q2r2s2t2 + 8q2r2s2t2x = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -4q2r2s2t2 + 8q2r2s2t2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -2q2r2s2t2 + 4q2r2s2t2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2q2r2s2t2 + 4q2r2s2t2x)' equal to zero and attempt to solve: Simplifying -1 + -2q2r2s2t2 + 4q2r2s2t2x = 0 Solving -1 + -2q2r2s2t2 + 4q2r2s2t2x = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -2q2r2s2t2 + 1 + 4q2r2s2t2x = 0 + 1 Reorder the terms: -1 + 1 + -2q2r2s2t2 + 4q2r2s2t2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2q2r2s2t2 + 4q2r2s2t2x = 0 + 1 -2q2r2s2t2 + 4q2r2s2t2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2q2r2s2t2 + 4q2r2s2t2x = 1 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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