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Simplifying sqrt(x2 + -5x + 6) + sqrt(x + -3) + sqrt(x + 21) = sqrt((x + -2)(x + 21)) Reorder the terms: qrst(6 + -5x + x2) + sqrt(x + -3) + sqrt(x + 21) = sqrt((x + -2)(x + 21)) (6 * qrst + -5x * qrst + x2 * qrst) + sqrt(x + -3) + sqrt(x + 21) = sqrt((x + -2)(x + 21)) (6qrst + -5qrstx + qrstx2) + sqrt(x + -3) + sqrt(x + 21) = sqrt((x + -2)(x + 21)) Reorder the terms: 6qrst + -5qrstx + qrstx2 + qrst(-3 + x) + sqrt(x + 21) = sqrt((x + -2)(x + 21)) 6qrst + -5qrstx + qrstx2 + (-3 * qrst + x * qrst) + sqrt(x + 21) = sqrt((x + -2)(x + 21)) 6qrst + -5qrstx + qrstx2 + (-3qrst + qrstx) + sqrt(x + 21) = sqrt((x + -2)(x + 21)) Reorder the terms: 6qrst + -5qrstx + qrstx2 + -3qrst + qrstx + qrst(21 + x) = sqrt((x + -2)(x + 21)) 6qrst + -5qrstx + qrstx2 + -3qrst + qrstx + (21 * qrst + x * qrst) = sqrt((x + -2)(x + 21)) 6qrst + -5qrstx + qrstx2 + -3qrst + qrstx + (21qrst + qrstx) = sqrt((x + -2)(x + 21)) Reorder the terms: 6qrst + -3qrst + 21qrst + -5qrstx + qrstx + qrstx + qrstx2 = sqrt((x + -2)(x + 21)) Combine like terms: 6qrst + -3qrst = 3qrst 3qrst + 21qrst + -5qrstx + qrstx + qrstx + qrstx2 = sqrt((x + -2)(x + 21)) Combine like terms: 3qrst + 21qrst = 24qrst 24qrst + -5qrstx + qrstx + qrstx + qrstx2 = sqrt((x + -2)(x + 21)) Combine like terms: -5qrstx + qrstx = -4qrstx 24qrst + -4qrstx + qrstx + qrstx2 = sqrt((x + -2)(x + 21)) Combine like terms: -4qrstx + qrstx = -3qrstx 24qrst + -3qrstx + qrstx2 = sqrt((x + -2)(x + 21)) Reorder the terms: 24qrst + -3qrstx + qrstx2 = qrst((-2 + x)(x + 21)) Reorder the terms: 24qrst + -3qrstx + qrstx2 = qrst((-2 + x)(21 + x)) Multiply (-2 + x) * (21 + x) 24qrst + -3qrstx + qrstx2 = qrst((-2(21 + x) + x(21 + x))) 24qrst + -3qrstx + qrstx2 = qrst(((21 * -2 + x * -2) + x(21 + x))) 24qrst + -3qrstx + qrstx2 = qrst(((-42 + -2x) + x(21 + x))) 24qrst + -3qrstx + qrstx2 = qrst((-42 + -2x + (21 * x + x * x))) 24qrst + -3qrstx + qrstx2 = qrst((-42 + -2x + (21x + x2))) Combine like terms: -2x + 21x = 19x 24qrst + -3qrstx + qrstx2 = qrst((-42 + 19x + x2)) 24qrst + -3qrstx + qrstx2 = (-42 * qrst + 19x * qrst + x2 * qrst) 24qrst + -3qrstx + qrstx2 = (-42qrst + 19qrstx + qrstx2) Add '-1qrstx2' to each side of the equation. 24qrst + -3qrstx + qrstx2 + -1qrstx2 = -42qrst + 19qrstx + qrstx2 + -1qrstx2 Combine like terms: qrstx2 + -1qrstx2 = 0 24qrst + -3qrstx + 0 = -42qrst + 19qrstx + qrstx2 + -1qrstx2 24qrst + -3qrstx = -42qrst + 19qrstx + qrstx2 + -1qrstx2 Combine like terms: qrstx2 + -1qrstx2 = 0 24qrst + -3qrstx = -42qrst + 19qrstx + 0 24qrst + -3qrstx = -42qrst + 19qrstx Solving 24qrst + -3qrstx = -42qrst + 19qrstx Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '42qrst' to each side of the equation. 24qrst + 42qrst + -3qrstx = -42qrst + 42qrst + 19qrstx Combine like terms: 24qrst + 42qrst = 66qrst 66qrst + -3qrstx = -42qrst + 42qrst + 19qrstx Combine like terms: -42qrst + 42qrst = 0 66qrst + -3qrstx = 0 + 19qrstx 66qrst + -3qrstx = 19qrstx Add '-19qrstx' to each side of the equation. 66qrst + -3qrstx + -19qrstx = 19qrstx + -19qrstx Combine like terms: -3qrstx + -19qrstx = -22qrstx 66qrst + -22qrstx = 19qrstx + -19qrstx Combine like terms: 19qrstx + -19qrstx = 0 66qrst + -22qrstx = 0 Factor out the Greatest Common Factor (GCF), '22qrst'. 22qrst(3 + -1x) = 0 Ignore the factor 22.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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