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Simplifying sqrt(x + 1) + sqrt(10 + -1x) = sqrt(2x + -7) Reorder the terms: qrst(1 + x) + sqrt(10 + -1x) = sqrt(2x + -7) (1 * qrst + x * qrst) + sqrt(10 + -1x) = sqrt(2x + -7) (1qrst + qrstx) + sqrt(10 + -1x) = sqrt(2x + -7) 1qrst + qrstx + (10 * qrst + -1x * qrst) = sqrt(2x + -7) 1qrst + qrstx + (10qrst + -1qrstx) = sqrt(2x + -7) Reorder the terms: 1qrst + 10qrst + qrstx + -1qrstx = sqrt(2x + -7) Combine like terms: 1qrst + 10qrst = 11qrst 11qrst + qrstx + -1qrstx = sqrt(2x + -7) Combine like terms: qrstx + -1qrstx = 0 11qrst + 0 = sqrt(2x + -7) 11qrst = sqrt(2x + -7) Reorder the terms: 11qrst = qrst(-7 + 2x) 11qrst = (-7 * qrst + 2x * qrst) 11qrst = (-7qrst + 2qrstx) Solving 11qrst = -7qrst + 2qrstx Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7qrst' to each side of the equation. 11qrst + 7qrst = -7qrst + 7qrst + 2qrstx Combine like terms: 11qrst + 7qrst = 18qrst 18qrst = -7qrst + 7qrst + 2qrstx Combine like terms: -7qrst + 7qrst = 0 18qrst = 0 + 2qrstx 18qrst = 2qrstx Add '-2qrstx' to each side of the equation. 18qrst + -2qrstx = 2qrstx + -2qrstx Combine like terms: 2qrstx + -2qrstx = 0 18qrst + -2qrstx = 0 Factor out the Greatest Common Factor (GCF), '2qrst'. 2qrst(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + 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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