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Simplifying sqrt(x + sqrt(2)) + -1sqrt(x + -1sqrt(2)) = sqrt(2) Reorder the terms for easier multiplication: qrst(x + 2qrst) + -1sqrt(x + -1sqrt(2)) = sqrt(2) Reorder the terms: qrst(2qrst + x) + -1sqrt(x + -1sqrt(2)) = sqrt(2) (2qrst * qrst + x * qrst) + -1sqrt(x + -1sqrt(2)) = sqrt(2) Reorder the terms: (qrstx + 2q2r2s2t2) + -1sqrt(x + -1sqrt(2)) = sqrt(2) (qrstx + 2q2r2s2t2) + -1sqrt(x + -1sqrt(2)) = sqrt(2) Reorder the terms for easier multiplication: qrstx + 2q2r2s2t2 + -1qrst(x + -1 * 2qrst) = sqrt(2) Multiply -1 * 2 qrstx + 2q2r2s2t2 + -1qrst(x + -2qrst) = sqrt(2) Reorder the terms: qrstx + 2q2r2s2t2 + -1qrst(-2qrst + x) = sqrt(2) qrstx + 2q2r2s2t2 + (-2qrst * -1qrst + x * -1qrst) = sqrt(2) Reorder the terms: qrstx + 2q2r2s2t2 + (-1qrstx + 2q2r2s2t2) = sqrt(2) qrstx + 2q2r2s2t2 + (-1qrstx + 2q2r2s2t2) = sqrt(2) Reorder the terms: qrstx + -1qrstx + 2q2r2s2t2 + 2q2r2s2t2 = sqrt(2) Combine like terms: qrstx + -1qrstx = 0 0 + 2q2r2s2t2 + 2q2r2s2t2 = sqrt(2) 2q2r2s2t2 + 2q2r2s2t2 = sqrt(2) Combine like terms: 2q2r2s2t2 + 2q2r2s2t2 = 4q2r2s2t2 4q2r2s2t2 = sqrt(2) Reorder the terms for easier multiplication: 4q2r2s2t2 = 2qrst Solving 4q2r2s2t2 = 2qrst Solving for variable 'q'. Reorder the terms: -2qrst + 4q2r2s2t2 = 2qrst + -2qrst Combine like terms: 2qrst + -2qrst = 0 -2qrst + 4q2r2s2t2 = 0 Factor out the Greatest Common Factor (GCF), '2qrst'. 2qrst(-1 + 2qrst) = 0 Ignore the factor 2.Subproblem 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 '(-1 + 2qrst)' equal to zero and attempt to solve: Simplifying -1 + 2qrst = 0 Solving -1 + 2qrst = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2qrst = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2qrst = 0 + 1 2qrst = 0 + 1 Combine like terms: 0 + 1 = 1 2qrst = 1 Divide each side by '2rst'. q = 0.5r-1s-1t-1 Simplifying q = 0.5r-1s-1t-1Solution
q = {0.5r-1s-1t-1}
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