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Simplifying sqrt(2x + 8) + sqrt(x + 3) = sqrt(6x + 13) Reorder the terms: qrst(8 + 2x) + sqrt(x + 3) = sqrt(6x + 13) (8 * qrst + 2x * qrst) + sqrt(x + 3) = sqrt(6x + 13) (8qrst + 2qrstx) + sqrt(x + 3) = sqrt(6x + 13) Reorder the terms: 8qrst + 2qrstx + qrst(3 + x) = sqrt(6x + 13) 8qrst + 2qrstx + (3 * qrst + x * qrst) = sqrt(6x + 13) 8qrst + 2qrstx + (3qrst + qrstx) = sqrt(6x + 13) Reorder the terms: 8qrst + 3qrst + 2qrstx + qrstx = sqrt(6x + 13) Combine like terms: 8qrst + 3qrst = 11qrst 11qrst + 2qrstx + qrstx = sqrt(6x + 13) Combine like terms: 2qrstx + qrstx = 3qrstx 11qrst + 3qrstx = sqrt(6x + 13) Reorder the terms: 11qrst + 3qrstx = qrst(13 + 6x) 11qrst + 3qrstx = (13 * qrst + 6x * qrst) 11qrst + 3qrstx = (13qrst + 6qrstx) Solving 11qrst + 3qrstx = 13qrst + 6qrstx Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-13qrst' to each side of the equation. 11qrst + -13qrst + 3qrstx = 13qrst + -13qrst + 6qrstx Combine like terms: 11qrst + -13qrst = -2qrst -2qrst + 3qrstx = 13qrst + -13qrst + 6qrstx Combine like terms: 13qrst + -13qrst = 0 -2qrst + 3qrstx = 0 + 6qrstx -2qrst + 3qrstx = 6qrstx Add '-6qrstx' to each side of the equation. -2qrst + 3qrstx + -6qrstx = 6qrstx + -6qrstx Combine like terms: 3qrstx + -6qrstx = -3qrstx -2qrst + -3qrstx = 6qrstx + -6qrstx Combine like terms: 6qrstx + -6qrstx = 0 -2qrst + -3qrstx = 0 Factor out the Greatest Common Factor (GCF), '-1qrst'. -1qrst(2 + 3x) = 0 Ignore the factor -1.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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Add '-3x' to each side of the equation. 3x + -3x = -2 + -3x Combine like terms: 3x + -3x = 0 0 = -2 + -3x Simplifying 0 = -2 + -3x 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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