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Simplifying sqrt(x + 2) + sqrt(2 + -4x) = sqrt(10) Reorder the terms: qrst(2 + x) + sqrt(2 + -4x) = sqrt(10) (2 * qrst + x * qrst) + sqrt(2 + -4x) = sqrt(10) (2qrst + qrstx) + sqrt(2 + -4x) = sqrt(10) 2qrst + qrstx + (2 * qrst + -4x * qrst) = sqrt(10) 2qrst + qrstx + (2qrst + -4qrstx) = sqrt(10) Reorder the terms: 2qrst + 2qrst + qrstx + -4qrstx = sqrt(10) Combine like terms: 2qrst + 2qrst = 4qrst 4qrst + qrstx + -4qrstx = sqrt(10) Combine like terms: qrstx + -4qrstx = -3qrstx 4qrst + -3qrstx = sqrt(10) Reorder the terms for easier multiplication: 4qrst + -3qrstx = 10qrst Solving 4qrst + -3qrstx = 10qrst Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-10qrst' to each side of the equation. 4qrst + -10qrst + -3qrstx = 10qrst + -10qrst Combine like terms: 4qrst + -10qrst = -6qrst -6qrst + -3qrstx = 10qrst + -10qrst Combine like terms: 10qrst + -10qrst = 0 -6qrst + -3qrstx = 0 Factor out the Greatest Common Factor (GCF), '-3qrst'. -3qrst(2 + x) = 0 Ignore the factor -3.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + 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 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -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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