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Simplifying Sqrt(5p + 5) = sqrt(6p + 3) Reorder the terms: qrtS(5 + 5p) = sqrt(6p + 3) (5 * qrtS + 5p * qrtS) = sqrt(6p + 3) Reorder the terms: (5pqrtS + 5qrtS) = sqrt(6p + 3) (5pqrtS + 5qrtS) = sqrt(6p + 3) Reorder the terms: 5pqrtS + 5qrtS = qrst(3 + 6p) 5pqrtS + 5qrtS = (3 * qrst + 6p * qrst) Reorder the terms: 5pqrtS + 5qrtS = (6pqrst + 3qrst) 5pqrtS + 5qrtS = (6pqrst + 3qrst) Solving 5pqrtS + 5qrtS = 6pqrst + 3qrst Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6pqrst' to each side of the equation. 5pqrtS + -6pqrst + 5qrtS = 6pqrst + -6pqrst + 3qrst Reorder the terms: -6pqrst + 5pqrtS + 5qrtS = 6pqrst + -6pqrst + 3qrst Combine like terms: 6pqrst + -6pqrst = 0 -6pqrst + 5pqrtS + 5qrtS = 0 + 3qrst -6pqrst + 5pqrtS + 5qrtS = 3qrst Add '-5qrtS' to each side of the equation. -6pqrst + 5pqrtS + 5qrtS + -5qrtS = 3qrst + -5qrtS Combine like terms: 5qrtS + -5qrtS = 0 -6pqrst + 5pqrtS + 0 = 3qrst + -5qrtS -6pqrst + 5pqrtS = 3qrst + -5qrtS Reorder the terms: -6pqrst + 5pqrtS + -3qrst + 5qrtS = 3qrst + -3qrst + -5qrtS + 5qrtS Combine like terms: 3qrst + -3qrst = 0 -6pqrst + 5pqrtS + -3qrst + 5qrtS = 0 + -5qrtS + 5qrtS -6pqrst + 5pqrtS + -3qrst + 5qrtS = -5qrtS + 5qrtS Combine like terms: -5qrtS + 5qrtS = 0 -6pqrst + 5pqrtS + -3qrst + 5qrtS = 0 Factor out the Greatest Common Factor (GCF), 'qrt'. qrt(-6ps + 5pS + -3s + 5S) = 0Subproblem 1
Set the factor 'qrt' equal to zero and attempt to solve: Simplifying qrt = 0 Solving qrt = 0 Move all terms containing p to the left, all other terms to the right. Add '-1qrt' to each side of the equation. qrt + -1qrt = 0 + -1qrt Remove the zero: 0 = -1qrt Simplifying 0 = -1qrt 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 '(-6ps + 5pS + -3s + 5S)' equal to zero and attempt to solve: Simplifying -6ps + 5pS + -3s + 5S = 0 Reorder the terms: 5S + 5pS + -6ps + -3s = 0 Solving 5S + 5pS + -6ps + -3s = 0 Move all terms containing p to the left, all other terms to the right. Add '-5S' to each side of the equation. 5S + 5pS + -6ps + -5S + -3s = 0 + -5S Reorder the terms: 5S + -5S + 5pS + -6ps + -3s = 0 + -5S Combine like terms: 5S + -5S = 0 0 + 5pS + -6ps + -3s = 0 + -5S 5pS + -6ps + -3s = 0 + -5S Remove the zero: 5pS + -6ps + -3s = -5S Add '3s' to each side of the equation. 5pS + -6ps + -3s + 3s = -5S + 3s Combine like terms: -3s + 3s = 0 5pS + -6ps + 0 = -5S + 3s 5pS + -6ps = -5S + 3s 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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