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Simplifying sqrt(10x + 9) = sqrt(4x + 6) Reorder the terms: qrst(9 + 10x) = sqrt(4x + 6) (9 * qrst + 10x * qrst) = sqrt(4x + 6) (9qrst + 10qrstx) = sqrt(4x + 6) Reorder the terms: 9qrst + 10qrstx = qrst(6 + 4x) 9qrst + 10qrstx = (6 * qrst + 4x * qrst) 9qrst + 10qrstx = (6qrst + 4qrstx) Solving 9qrst + 10qrstx = 6qrst + 4qrstx Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-6qrst' to each side of the equation. 9qrst + -6qrst + 10qrstx = 6qrst + -6qrst + 4qrstx Combine like terms: 9qrst + -6qrst = 3qrst 3qrst + 10qrstx = 6qrst + -6qrst + 4qrstx Combine like terms: 6qrst + -6qrst = 0 3qrst + 10qrstx = 0 + 4qrstx 3qrst + 10qrstx = 4qrstx Add '-4qrstx' to each side of the equation. 3qrst + 10qrstx + -4qrstx = 4qrstx + -4qrstx Combine like terms: 10qrstx + -4qrstx = 6qrstx 3qrst + 6qrstx = 4qrstx + -4qrstx Combine like terms: 4qrstx + -4qrstx = 0 3qrst + 6qrstx = 0 Factor out the Greatest Common Factor (GCF), '3qrst'. 3qrst(1 + 2x) = 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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