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Simplifying sqrt(x + -1) + sqrt(x + 3) + 2sqrt((x + -1)(x + 3)) = 4 + -2x Reorder the terms: qrst(-1 + x) + sqrt(x + 3) + 2sqrt((x + -1)(x + 3)) = 4 + -2x (-1 * qrst + x * qrst) + sqrt(x + 3) + 2sqrt((x + -1)(x + 3)) = 4 + -2x (-1qrst + qrstx) + sqrt(x + 3) + 2sqrt((x + -1)(x + 3)) = 4 + -2x Reorder the terms: -1qrst + qrstx + qrst(3 + x) + 2sqrt((x + -1)(x + 3)) = 4 + -2x -1qrst + qrstx + (3 * qrst + x * qrst) + 2sqrt((x + -1)(x + 3)) = 4 + -2x -1qrst + qrstx + (3qrst + qrstx) + 2sqrt((x + -1)(x + 3)) = 4 + -2x Reorder the terms: -1qrst + qrstx + 3qrst + qrstx + 2qrst((-1 + x)(x + 3)) = 4 + -2x Reorder the terms: -1qrst + qrstx + 3qrst + qrstx + 2qrst((-1 + x)(3 + x)) = 4 + -2x Multiply (-1 + x) * (3 + x) -1qrst + qrstx + 3qrst + qrstx + 2qrst((-1(3 + x) + x(3 + x))) = 4 + -2x -1qrst + qrstx + 3qrst + qrstx + 2qrst(((3 * -1 + x * -1) + x(3 + x))) = 4 + -2x -1qrst + qrstx + 3qrst + qrstx + 2qrst(((-3 + -1x) + x(3 + x))) = 4 + -2x -1qrst + qrstx + 3qrst + qrstx + 2qrst((-3 + -1x + (3 * x + x * x))) = 4 + -2x -1qrst + qrstx + 3qrst + qrstx + 2qrst((-3 + -1x + (3x + x2))) = 4 + -2x Combine like terms: -1x + 3x = 2x -1qrst + qrstx + 3qrst + qrstx + 2qrst((-3 + 2x + x2)) = 4 + -2x -1qrst + qrstx + 3qrst + qrstx + (-3 * 2qrst + 2x * 2qrst + x2 * 2qrst) = 4 + -2x -1qrst + qrstx + 3qrst + qrstx + (-6qrst + 4qrstx + 2qrstx2) = 4 + -2x Reorder the terms: -1qrst + 3qrst + -6qrst + qrstx + qrstx + 4qrstx + 2qrstx2 = 4 + -2x Combine like terms: -1qrst + 3qrst = 2qrst 2qrst + -6qrst + qrstx + qrstx + 4qrstx + 2qrstx2 = 4 + -2x Combine like terms: 2qrst + -6qrst = -4qrst -4qrst + qrstx + qrstx + 4qrstx + 2qrstx2 = 4 + -2x Combine like terms: qrstx + qrstx = 2qrstx -4qrst + 2qrstx + 4qrstx + 2qrstx2 = 4 + -2x Combine like terms: 2qrstx + 4qrstx = 6qrstx -4qrst + 6qrstx + 2qrstx2 = 4 + -2x Solving -4qrst + 6qrstx + 2qrstx2 = 4 + -2x Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Reorder the terms: -4 + -4qrst + 6qrstx + 2qrstx2 + 2x = 4 + -2x + -4 + 2x Reorder the terms: -4 + -4qrst + 6qrstx + 2qrstx2 + 2x = 4 + -4 + -2x + 2x Combine like terms: 4 + -4 = 0 -4 + -4qrst + 6qrstx + 2qrstx2 + 2x = 0 + -2x + 2x -4 + -4qrst + 6qrstx + 2qrstx2 + 2x = -2x + 2x Combine like terms: -2x + 2x = 0 -4 + -4qrst + 6qrstx + 2qrstx2 + 2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -2qrst + 3qrstx + qrstx2 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -2qrst + 3qrstx + qrstx2 + x)' equal to zero and attempt to solve: Simplifying -2 + -2qrst + 3qrstx + qrstx2 + x = 0 Solving -2 + -2qrst + 3qrstx + qrstx2 + x = 0 Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -2qrst + 3qrstx + qrstx2 + 2 + x = 0 + 2 Reorder the terms: -2 + 2 + -2qrst + 3qrstx + qrstx2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2qrst + 3qrstx + qrstx2 + x = 0 + 2 -2qrst + 3qrstx + qrstx2 + x = 0 + 2 Combine like terms: 0 + 2 = 2 -2qrst + 3qrstx + qrstx2 + x = 2 Add '-1x' to each side of the equation. -2qrst + 3qrstx + qrstx2 + x + -1x = 2 + -1x Combine like terms: x + -1x = 0 -2qrst + 3qrstx + qrstx2 + 0 = 2 + -1x -2qrst + 3qrstx + qrstx2 = 2 + -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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