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Simplifying sqrt(2x + 3) + 2 = sqrt(6x + 7) Reorder the terms: qrst(3 + 2x) + 2 = sqrt(6x + 7) (3 * qrst + 2x * qrst) + 2 = sqrt(6x + 7) (3qrst + 2qrstx) + 2 = sqrt(6x + 7) Reorder the terms: 2 + 3qrst + 2qrstx = sqrt(6x + 7) Reorder the terms: 2 + 3qrst + 2qrstx = qrst(7 + 6x) 2 + 3qrst + 2qrstx = (7 * qrst + 6x * qrst) 2 + 3qrst + 2qrstx = (7qrst + 6qrstx) Solving 2 + 3qrst + 2qrstx = 7qrst + 6qrstx Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-7qrst' to each side of the equation. 2 + 3qrst + -7qrst + 2qrstx = 7qrst + -7qrst + 6qrstx Combine like terms: 3qrst + -7qrst = -4qrst 2 + -4qrst + 2qrstx = 7qrst + -7qrst + 6qrstx Combine like terms: 7qrst + -7qrst = 0 2 + -4qrst + 2qrstx = 0 + 6qrstx 2 + -4qrst + 2qrstx = 6qrstx Add '-6qrstx' to each side of the equation. 2 + -4qrst + 2qrstx + -6qrstx = 6qrstx + -6qrstx Combine like terms: 2qrstx + -6qrstx = -4qrstx 2 + -4qrst + -4qrstx = 6qrstx + -6qrstx Combine like terms: 6qrstx + -6qrstx = 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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