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Simplifying sqrt(5x + -1) + sqrt(3 + -1x) = 2(3x + -2) Reorder the terms: qrst(-1 + 5x) + sqrt(3 + -1x) = 2(3x + -2) (-1 * qrst + 5x * qrst) + sqrt(3 + -1x) = 2(3x + -2) (-1qrst + 5qrstx) + sqrt(3 + -1x) = 2(3x + -2) -1qrst + 5qrstx + (3 * qrst + -1x * qrst) = 2(3x + -2) -1qrst + 5qrstx + (3qrst + -1qrstx) = 2(3x + -2) Reorder the terms: -1qrst + 3qrst + 5qrstx + -1qrstx = 2(3x + -2) Combine like terms: -1qrst + 3qrst = 2qrst 2qrst + 5qrstx + -1qrstx = 2(3x + -2) Combine like terms: 5qrstx + -1qrstx = 4qrstx 2qrst + 4qrstx = 2(3x + -2) Reorder the terms: 2qrst + 4qrstx = 2(-2 + 3x) 2qrst + 4qrstx = (-2 * 2 + 3x * 2) 2qrst + 4qrstx = (-4 + 6x) Solving 2qrst + 4qrstx = -4 + 6x Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Reorder the terms: 4 + 2qrst + 4qrstx + -6x = -4 + 6x + 4 + -6x Reorder the terms: 4 + 2qrst + 4qrstx + -6x = -4 + 4 + 6x + -6x Combine like terms: -4 + 4 = 0 4 + 2qrst + 4qrstx + -6x = 0 + 6x + -6x 4 + 2qrst + 4qrstx + -6x = 6x + -6x Combine like terms: 6x + -6x = 0 4 + 2qrst + 4qrstx + -6x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + qrst + 2qrstx + -3x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + qrst + 2qrstx + -3x)' equal to zero and attempt to solve: Simplifying 2 + qrst + 2qrstx + -3x = 0 Solving 2 + qrst + 2qrstx + -3x = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + qrst + 2qrstx + -2 + -3x = 0 + -2 Reorder the terms: 2 + -2 + qrst + 2qrstx + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + qrst + 2qrstx + -3x = 0 + -2 qrst + 2qrstx + -3x = 0 + -2 Combine like terms: 0 + -2 = -2 qrst + 2qrstx + -3x = -2 Add '3x' to each side of the equation. qrst + 2qrstx + -3x + 3x = -2 + 3x Combine like terms: -3x + 3x = 0 qrst + 2qrstx + 0 = -2 + 3x qrst + 2qrstx = -2 + 3x 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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