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Simplifying sqrt(z) + sqrt(z + -3) = sqrt(z + 5) Multiply qrst * z qrstz + sqrt(z + -3) = sqrt(z + 5) Reorder the terms: qrstz + qrst(-3 + z) = sqrt(z + 5) qrstz + (-3 * qrst + z * qrst) = sqrt(z + 5) qrstz + (-3qrst + qrstz) = sqrt(z + 5) Reorder the terms: -3qrst + qrstz + qrstz = sqrt(z + 5) Combine like terms: qrstz + qrstz = 2qrstz -3qrst + 2qrstz = sqrt(z + 5) Reorder the terms: -3qrst + 2qrstz = qrst(5 + z) -3qrst + 2qrstz = (5 * qrst + z * qrst) -3qrst + 2qrstz = (5qrst + qrstz) Solving -3qrst + 2qrstz = 5qrst + qrstz Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-5qrst' to each side of the equation. -3qrst + -5qrst + 2qrstz = 5qrst + -5qrst + qrstz Combine like terms: -3qrst + -5qrst = -8qrst -8qrst + 2qrstz = 5qrst + -5qrst + qrstz Combine like terms: 5qrst + -5qrst = 0 -8qrst + 2qrstz = 0 + qrstz -8qrst + 2qrstz = qrstz Add '-1qrstz' to each side of the equation. -8qrst + 2qrstz + -1qrstz = qrstz + -1qrstz Combine like terms: 2qrstz + -1qrstz = 1qrstz -8qrst + 1qrstz = qrstz + -1qrstz Combine like terms: qrstz + -1qrstz = 0 -8qrst + 1qrstz = 0 Factor out the Greatest Common Factor (GCF), 'qrst'. qrst(-8 + z) = 0Subproblem 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 '(-8 + z)' equal to zero and attempt to solve: Simplifying -8 + z = 0 Solving -8 + z = 0 Move all terms containing q to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + z = 0 + 8 z = 0 + 8 Combine like terms: 0 + 8 = 8 z = 8 Add '-1z' to each side of the equation. z + -1z = 8 + -1z Combine like terms: z + -1z = 0 0 = 8 + -1z Simplifying 0 = 8 + -1z 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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