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Simplifying sqrt(6x + 7) + -2 = sqrt(2x + 3) Reorder the terms: qrst(7 + 6x) + -2 = sqrt(2x + 3) (7 * qrst + 6x * qrst) + -2 = sqrt(2x + 3) (7qrst + 6qrstx) + -2 = sqrt(2x + 3) Reorder the terms: -2 + 7qrst + 6qrstx = sqrt(2x + 3) Reorder the terms: -2 + 7qrst + 6qrstx = qrst(3 + 2x) -2 + 7qrst + 6qrstx = (3 * qrst + 2x * qrst) -2 + 7qrst + 6qrstx = (3qrst + 2qrstx) Solving -2 + 7qrst + 6qrstx = 3qrst + 2qrstx Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3qrst' to each side of the equation. -2 + 7qrst + -3qrst + 6qrstx = 3qrst + -3qrst + 2qrstx Combine like terms: 7qrst + -3qrst = 4qrst -2 + 4qrst + 6qrstx = 3qrst + -3qrst + 2qrstx Combine like terms: 3qrst + -3qrst = 0 -2 + 4qrst + 6qrstx = 0 + 2qrstx -2 + 4qrst + 6qrstx = 2qrstx Add '-2qrstx' to each side of the equation. -2 + 4qrst + 6qrstx + -2qrstx = 2qrstx + -2qrstx Combine like terms: 6qrstx + -2qrstx = 4qrstx -2 + 4qrst + 4qrstx = 2qrstx + -2qrstx Combine like terms: 2qrstx + -2qrstx = 0 -2 + 4qrst + 4qrstx = 0 Add '2' to each side of the equation. -2 + 4qrst + 2 + 4qrstx = 0 + 2 Reorder the terms: -2 + 2 + 4qrst + 4qrstx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4qrst + 4qrstx = 0 + 2 4qrst + 4qrstx = 0 + 2 Combine like terms: 0 + 2 = 2 4qrst + 4qrstx = 2 Reorder the terms: -2 + 4qrst + 4qrstx = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 4qrst + 4qrstx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2qrst + 2qrstx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 2qrst + 2qrstx)' equal to zero and attempt to solve: Simplifying -1 + 2qrst + 2qrstx = 0 Solving -1 + 2qrst + 2qrstx = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 2qrst + 1 + 2qrstx = 0 + 1 Reorder the terms: -1 + 1 + 2qrst + 2qrstx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2qrst + 2qrstx = 0 + 1 2qrst + 2qrstx = 0 + 1 Combine like terms: 0 + 1 = 1 2qrst + 2qrstx = 1 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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