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Simplifying sqrt(x + 1) + sqrt(2x) = sqrt(5x + 3) Reorder the terms: qrst(1 + x) + sqrt(2x) = sqrt(5x + 3) (1 * qrst + x * qrst) + sqrt(2x) = sqrt(5x + 3) (1qrst + qrstx) + sqrt(2x) = sqrt(5x + 3) Remove parenthesis around (2x) 1qrst + qrstx + qrst * 2x = sqrt(5x + 3) Reorder the terms for easier multiplication: 1qrst + qrstx + 2qrst * x = sqrt(5x + 3) Multiply qrst * x 1qrst + qrstx + 2qrstx = sqrt(5x + 3) Combine like terms: qrstx + 2qrstx = 3qrstx 1qrst + 3qrstx = sqrt(5x + 3) Reorder the terms: 1qrst + 3qrstx = qrst(3 + 5x) 1qrst + 3qrstx = (3 * qrst + 5x * qrst) 1qrst + 3qrstx = (3qrst + 5qrstx) Solving 1qrst + 3qrstx = 3qrst + 5qrstx 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. 1qrst + -3qrst + 3qrstx = 3qrst + -3qrst + 5qrstx Combine like terms: 1qrst + -3qrst = -2qrst -2qrst + 3qrstx = 3qrst + -3qrst + 5qrstx Combine like terms: 3qrst + -3qrst = 0 -2qrst + 3qrstx = 0 + 5qrstx -2qrst + 3qrstx = 5qrstx Add '-5qrstx' to each side of the equation. -2qrst + 3qrstx + -5qrstx = 5qrstx + -5qrstx Combine like terms: 3qrstx + -5qrstx = -2qrstx -2qrst + -2qrstx = 5qrstx + -5qrstx Combine like terms: 5qrstx + -5qrstx = 0 -2qrst + -2qrstx = 0 Factor out the Greatest Common Factor (GCF), '-2qrst'. -2qrst(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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