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Simplifying 3x(sqrt(x + 12)) + 6(x + 12)(sqrt(x + 12)) = 0 Reorder the terms: 3x(qrst(12 + x)) + 6(x + 12)(sqrt(x + 12)) = 0 3x((12 * qrst + x * qrst)) + 6(x + 12)(sqrt(x + 12)) = 0 3x((12qrst + qrstx)) + 6(x + 12)(sqrt(x + 12)) = 0 (12qrst * 3x + qrstx * 3x) + 6(x + 12)(sqrt(x + 12)) = 0 (36qrstx + 3qrstx2) + 6(x + 12)(sqrt(x + 12)) = 0 Reorder the terms: 36qrstx + 3qrstx2 + 6(12 + x)(sqrt(x + 12)) = 0 Reorder the terms: 36qrstx + 3qrstx2 + 6(12 + x)(qrst(12 + x)) = 0 36qrstx + 3qrstx2 + 6(12 + x)((12 * qrst + x * qrst)) = 0 36qrstx + 3qrstx2 + 6(12 + x)((12qrst + qrstx)) = 0 Multiply (12 + x) * (12qrst + qrstx) 36qrstx + 3qrstx2 + 6(12(12qrst + qrstx) + x(12qrst + qrstx)) = 0 36qrstx + 3qrstx2 + 6((12qrst * 12 + qrstx * 12) + x(12qrst + qrstx)) = 0 36qrstx + 3qrstx2 + 6((144qrst + 12qrstx) + x(12qrst + qrstx)) = 0 36qrstx + 3qrstx2 + 6(144qrst + 12qrstx + (12qrst * x + qrstx * x)) = 0 36qrstx + 3qrstx2 + 6(144qrst + 12qrstx + (12qrstx + qrstx2)) = 0 Combine like terms: 12qrstx + 12qrstx = 24qrstx 36qrstx + 3qrstx2 + 6(144qrst + 24qrstx + qrstx2) = 0 36qrstx + 3qrstx2 + (144qrst * 6 + 24qrstx * 6 + qrstx2 * 6) = 0 36qrstx + 3qrstx2 + (864qrst + 144qrstx + 6qrstx2) = 0 Reorder the terms: 864qrst + 36qrstx + 144qrstx + 3qrstx2 + 6qrstx2 = 0 Combine like terms: 36qrstx + 144qrstx = 180qrstx 864qrst + 180qrstx + 3qrstx2 + 6qrstx2 = 0 Combine like terms: 3qrstx2 + 6qrstx2 = 9qrstx2 864qrst + 180qrstx + 9qrstx2 = 0 Solving 864qrst + 180qrstx + 9qrstx2 = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '9qrst'. 9qrst(96 + 20x + x2) = 0 Factor a trinomial. 9qrst((12 + x)(8 + x)) = 0 Ignore the factor 9.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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing q to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Add '-1x' to each side of the equation. x + -1x = -12 + -1x Combine like terms: x + -1x = 0 0 = -12 + -1x Simplifying 0 = -12 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -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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