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Simplifying sqrt(5x + 1) + sqrt(x + 6) = sqrt(2x + 3) + sqrt(6x + -2) Reorder the terms: qrst(1 + 5x) + sqrt(x + 6) = sqrt(2x + 3) + sqrt(6x + -2) (1 * qrst + 5x * qrst) + sqrt(x + 6) = sqrt(2x + 3) + sqrt(6x + -2) (1qrst + 5qrstx) + sqrt(x + 6) = sqrt(2x + 3) + sqrt(6x + -2) Reorder the terms: 1qrst + 5qrstx + qrst(6 + x) = sqrt(2x + 3) + sqrt(6x + -2) 1qrst + 5qrstx + (6 * qrst + x * qrst) = sqrt(2x + 3) + sqrt(6x + -2) 1qrst + 5qrstx + (6qrst + qrstx) = sqrt(2x + 3) + sqrt(6x + -2) Reorder the terms: 1qrst + 6qrst + 5qrstx + qrstx = sqrt(2x + 3) + sqrt(6x + -2) Combine like terms: 1qrst + 6qrst = 7qrst 7qrst + 5qrstx + qrstx = sqrt(2x + 3) + sqrt(6x + -2) Combine like terms: 5qrstx + qrstx = 6qrstx 7qrst + 6qrstx = sqrt(2x + 3) + sqrt(6x + -2) Reorder the terms: 7qrst + 6qrstx = qrst(3 + 2x) + sqrt(6x + -2) 7qrst + 6qrstx = (3 * qrst + 2x * qrst) + sqrt(6x + -2) 7qrst + 6qrstx = (3qrst + 2qrstx) + sqrt(6x + -2) Reorder the terms: 7qrst + 6qrstx = 3qrst + 2qrstx + qrst(-2 + 6x) 7qrst + 6qrstx = 3qrst + 2qrstx + (-2 * qrst + 6x * qrst) 7qrst + 6qrstx = 3qrst + 2qrstx + (-2qrst + 6qrstx) Reorder the terms: 7qrst + 6qrstx = 3qrst + -2qrst + 2qrstx + 6qrstx Combine like terms: 3qrst + -2qrst = 1qrst 7qrst + 6qrstx = 1qrst + 2qrstx + 6qrstx Combine like terms: 2qrstx + 6qrstx = 8qrstx 7qrst + 6qrstx = 1qrst + 8qrstx Solving 7qrst + 6qrstx = 1qrst + 8qrstx Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1qrst' to each side of the equation. 7qrst + -1qrst + 6qrstx = 1qrst + -1qrst + 8qrstx Combine like terms: 7qrst + -1qrst = 6qrst 6qrst + 6qrstx = 1qrst + -1qrst + 8qrstx Combine like terms: 1qrst + -1qrst = 0 6qrst + 6qrstx = 0 + 8qrstx 6qrst + 6qrstx = 8qrstx Add '-8qrstx' to each side of the equation. 6qrst + 6qrstx + -8qrstx = 8qrstx + -8qrstx Combine like terms: 6qrstx + -8qrstx = -2qrstx 6qrst + -2qrstx = 8qrstx + -8qrstx Combine like terms: 8qrstx + -8qrstx = 0 6qrst + -2qrstx = 0 Factor out the Greatest Common Factor (GCF), '2qrst'. 2qrst(3 + -1x) = 0 Ignore the factor 2.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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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