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Simplifying sqrt(2x + 7) = sqrt(5x + -8) Reorder the terms: qrst(7 + 2x) = sqrt(5x + -8) (7 * qrst + 2x * qrst) = sqrt(5x + -8) (7qrst + 2qrstx) = sqrt(5x + -8) Reorder the terms: 7qrst + 2qrstx = qrst(-8 + 5x) 7qrst + 2qrstx = (-8 * qrst + 5x * qrst) 7qrst + 2qrstx = (-8qrst + 5qrstx) Solving 7qrst + 2qrstx = -8qrst + 5qrstx Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '8qrst' to each side of the equation. 7qrst + 8qrst + 2qrstx = -8qrst + 8qrst + 5qrstx Combine like terms: 7qrst + 8qrst = 15qrst 15qrst + 2qrstx = -8qrst + 8qrst + 5qrstx Combine like terms: -8qrst + 8qrst = 0 15qrst + 2qrstx = 0 + 5qrstx 15qrst + 2qrstx = 5qrstx Add '-5qrstx' to each side of the equation. 15qrst + 2qrstx + -5qrstx = 5qrstx + -5qrstx Combine like terms: 2qrstx + -5qrstx = -3qrstx 15qrst + -3qrstx = 5qrstx + -5qrstx Combine like terms: 5qrstx + -5qrstx = 0 15qrst + -3qrstx = 0 Factor out the Greatest Common Factor (GCF), '3qrst'. 3qrst(5 + -1x) = 0 Ignore the factor 3.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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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