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Simplifying sqrt((x + 2) * sqrt(x + -1)) + sqrt((x + -2) * sqrt(x + -1)) = 6 Reorder the terms: qrst((2 + x) * sqrt(x + -1)) + sqrt((x + -2) * sqrt(x + -1)) = 6 Reorder the terms: qrst((2 + x) * qrst(-1 + x)) + sqrt((x + -2) * sqrt(x + -1)) = 6 Reorder the terms for easier multiplication: qrst(qrst(2 + x)(-1 + x)) + sqrt((x + -2) * sqrt(x + -1)) = 6 Multiply (2 + x) * (-1 + x) qrst(qrst(2(-1 + x) + x(-1 + x))) + sqrt((x + -2) * sqrt(x + -1)) = 6 qrst(qrst((-1 * 2 + x * 2) + x(-1 + x))) + sqrt((x + -2) * sqrt(x + -1)) = 6 qrst(qrst((-2 + 2x) + x(-1 + x))) + sqrt((x + -2) * sqrt(x + -1)) = 6 qrst(qrst(-2 + 2x + (-1 * x + x * x))) + sqrt((x + -2) * sqrt(x + -1)) = 6 qrst(qrst(-2 + 2x + (-1x + x2))) + sqrt((x + -2) * sqrt(x + -1)) = 6 Combine like terms: 2x + -1x = 1x qrst(qrst(-2 + 1x + x2)) + sqrt((x + -2) * sqrt(x + -1)) = 6 qrst((-2 * qrst + 1x * qrst + x2 * qrst)) + sqrt((x + -2) * sqrt(x + -1)) = 6 qrst((-2qrst + 1qrstx + qrstx2)) + sqrt((x + -2) * sqrt(x + -1)) = 6 (-2qrst * qrst + 1qrstx * qrst + qrstx2 * qrst) + sqrt((x + -2) * sqrt(x + -1)) = 6 (-2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2) + sqrt((x + -2) * sqrt(x + -1)) = 6 Reorder the terms: -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst((-2 + x) * sqrt(x + -1)) = 6 Reorder the terms: -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst((-2 + x) * qrst(-1 + x)) = 6 Reorder the terms for easier multiplication: -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst(qrst(-2 + x)(-1 + x)) = 6 Multiply (-2 + x) * (-1 + x) -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst(qrst(-2(-1 + x) + x(-1 + x))) = 6 -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst(qrst((-1 * -2 + x * -2) + x(-1 + x))) = 6 -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst(qrst((2 + -2x) + x(-1 + x))) = 6 -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst(qrst(2 + -2x + (-1 * x + x * x))) = 6 -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst(qrst(2 + -2x + (-1x + x2))) = 6 Combine like terms: -2x + -1x = -3x -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst(qrst(2 + -3x + x2)) = 6 -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst((2 * qrst + -3x * qrst + x2 * qrst)) = 6 -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + qrst((2qrst + -3qrstx + qrstx2)) = 6 -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + (2qrst * qrst + -3qrstx * qrst + qrstx2 * qrst) = 6 -2q2r2s2t2 + 1q2r2s2t2x + q2r2s2t2x2 + (2q2r2s2t2 + -3q2r2s2t2x + q2r2s2t2x2) = 6 Reorder the terms: -2q2r2s2t2 + 2q2r2s2t2 + 1q2r2s2t2x + -3q2r2s2t2x + q2r2s2t2x2 + q2r2s2t2x2 = 6 Combine like terms: -2q2r2s2t2 + 2q2r2s2t2 = 0 0 + 1q2r2s2t2x + -3q2r2s2t2x + q2r2s2t2x2 + q2r2s2t2x2 = 6 1q2r2s2t2x + -3q2r2s2t2x + q2r2s2t2x2 + q2r2s2t2x2 = 6 Combine like terms: 1q2r2s2t2x + -3q2r2s2t2x = -2q2r2s2t2x -2q2r2s2t2x + q2r2s2t2x2 + q2r2s2t2x2 = 6 Combine like terms: q2r2s2t2x2 + q2r2s2t2x2 = 2q2r2s2t2x2 -2q2r2s2t2x + 2q2r2s2t2x2 = 6 Solving -2q2r2s2t2x + 2q2r2s2t2x2 = 6 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Reorder the terms: -6 + -2q2r2s2t2x + 2q2r2s2t2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -2q2r2s2t2x + 2q2r2s2t2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -1q2r2s2t2x + q2r2s2t2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1q2r2s2t2x + q2r2s2t2x2)' equal to zero and attempt to solve: Simplifying -3 + -1q2r2s2t2x + q2r2s2t2x2 = 0 Solving -3 + -1q2r2s2t2x + q2r2s2t2x2 = 0 Move all terms containing q to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -1q2r2s2t2x + 3 + q2r2s2t2x2 = 0 + 3 Reorder the terms: -3 + 3 + -1q2r2s2t2x + q2r2s2t2x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1q2r2s2t2x + q2r2s2t2x2 = 0 + 3 -1q2r2s2t2x + q2r2s2t2x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1q2r2s2t2x + q2r2s2t2x2 = 3 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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