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Simplifying sqrt(2) * sqrt(x + 3) = sqrt(4x + -5) Reorder the terms: qrst * 2qrst(3 + x) = sqrt(4x + -5) Reorder the terms for easier multiplication: 2qrst * qrst(3 + x) = sqrt(4x + -5) Multiply qrst * qrst 2q2r2s2t2(3 + x) = sqrt(4x + -5) (3 * 2q2r2s2t2 + x * 2q2r2s2t2) = sqrt(4x + -5) (6q2r2s2t2 + 2q2r2s2t2x) = sqrt(4x + -5) Reorder the terms: 6q2r2s2t2 + 2q2r2s2t2x = qrst(-5 + 4x) 6q2r2s2t2 + 2q2r2s2t2x = (-5 * qrst + 4x * qrst) 6q2r2s2t2 + 2q2r2s2t2x = (-5qrst + 4qrstx) Solving 6q2r2s2t2 + 2q2r2s2t2x = -5qrst + 4qrstx Solving for variable 'q'. Reorder the terms: 5qrst + -4qrstx + 6q2r2s2t2 + 2q2r2s2t2x = -5qrst + 4qrstx + 5qrst + -4qrstx Reorder the terms: 5qrst + -4qrstx + 6q2r2s2t2 + 2q2r2s2t2x = -5qrst + 5qrst + 4qrstx + -4qrstx Combine like terms: -5qrst + 5qrst = 0 5qrst + -4qrstx + 6q2r2s2t2 + 2q2r2s2t2x = 0 + 4qrstx + -4qrstx 5qrst + -4qrstx + 6q2r2s2t2 + 2q2r2s2t2x = 4qrstx + -4qrstx Combine like terms: 4qrstx + -4qrstx = 0 5qrst + -4qrstx + 6q2r2s2t2 + 2q2r2s2t2x = 0 Factor out the Greatest Common Factor (GCF), 'qrst'. qrst(5 + -4x + 6qrst + 2qrstx) = 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 '(5 + -4x + 6qrst + 2qrstx)' equal to zero and attempt to solve: Simplifying 5 + -4x + 6qrst + 2qrstx = 0 Reorder the terms: 5 + 6qrst + 2qrstx + -4x = 0 Solving 5 + 6qrst + 2qrstx + -4x = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 6qrst + 2qrstx + -5 + -4x = 0 + -5 Reorder the terms: 5 + -5 + 6qrst + 2qrstx + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6qrst + 2qrstx + -4x = 0 + -5 6qrst + 2qrstx + -4x = 0 + -5 Combine like terms: 0 + -5 = -5 6qrst + 2qrstx + -4x = -5 Add '4x' to each side of the equation. 6qrst + 2qrstx + -4x + 4x = -5 + 4x Combine like terms: -4x + 4x = 0 6qrst + 2qrstx + 0 = -5 + 4x 6qrst + 2qrstx = -5 + 4x 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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