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Simplifying Sqrt[2x + 7] + Sqrt[3x + -18] = Sqrt[7x + 1] Reorder the terms: qrtS[7 + 2x] + Sqrt[3x + -18] = Sqrt[7x + 1] [7 * qrtS + 2x * qrtS] + Sqrt[3x + -18] = Sqrt[7x + 1] [7qrtS + 2qrtxS] + Sqrt[3x + -18] = Sqrt[7x + 1] Reorder the terms: 7qrtS + 2qrtxS + qrtS[-18 + 3x] = Sqrt[7x + 1] 7qrtS + 2qrtxS + [-18 * qrtS + 3x * qrtS] = Sqrt[7x + 1] 7qrtS + 2qrtxS + [-18qrtS + 3qrtxS] = Sqrt[7x + 1] Reorder the terms: 7qrtS + -18qrtS + 2qrtxS + 3qrtxS = Sqrt[7x + 1] Combine like terms: 7qrtS + -18qrtS = -11qrtS -11qrtS + 2qrtxS + 3qrtxS = Sqrt[7x + 1] Combine like terms: 2qrtxS + 3qrtxS = 5qrtxS -11qrtS + 5qrtxS = Sqrt[7x + 1] Reorder the terms: -11qrtS + 5qrtxS = qrtS[1 + 7x] -11qrtS + 5qrtxS = [1 * qrtS + 7x * qrtS] -11qrtS + 5qrtxS = [1qrtS + 7qrtxS] Solving -11qrtS + 5qrtxS = 1qrtS + 7qrtxS Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1qrtS' to each side of the equation. -11qrtS + -1qrtS + 5qrtxS = 1qrtS + -1qrtS + 7qrtxS Combine like terms: -11qrtS + -1qrtS = -12qrtS -12qrtS + 5qrtxS = 1qrtS + -1qrtS + 7qrtxS Combine like terms: 1qrtS + -1qrtS = 0 -12qrtS + 5qrtxS = 0 + 7qrtxS -12qrtS + 5qrtxS = 7qrtxS Add '-7qrtxS' to each side of the equation. -12qrtS + 5qrtxS + -7qrtxS = 7qrtxS + -7qrtxS Combine like terms: 5qrtxS + -7qrtxS = -2qrtxS -12qrtS + -2qrtxS = 7qrtxS + -7qrtxS Combine like terms: 7qrtxS + -7qrtxS = 0 -12qrtS + -2qrtxS = 0 Factor out the Greatest Common Factor (GCF), '-2qrtS'. -2qrtS(6 + x) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'qrtS' equal to zero and attempt to solve: Simplifying qrtS = 0 Solving qrtS = 0 Move all terms containing q to the left, all other terms to the right. Simplifying qrtS = 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x 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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