sqrt(4y+6)+sqrt(y+5)=sqrt(y+1)

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Solution for sqrt(4y+6)+sqrt(y+5)=sqrt(y+1) equation:


Simplifying
sqrt(4y + 6) + sqrt(y + 5) = sqrt(y + 1)

Reorder the terms:
qrst(6 + 4y) + sqrt(y + 5) = sqrt(y + 1)
(6 * qrst + 4y * qrst) + sqrt(y + 5) = sqrt(y + 1)
(6qrst + 4qrsty) + sqrt(y + 5) = sqrt(y + 1)

Reorder the terms:
6qrst + 4qrsty + qrst(5 + y) = sqrt(y + 1)
6qrst + 4qrsty + (5 * qrst + y * qrst) = sqrt(y + 1)
6qrst + 4qrsty + (5qrst + qrsty) = sqrt(y + 1)

Reorder the terms:
6qrst + 5qrst + 4qrsty + qrsty = sqrt(y + 1)

Combine like terms: 6qrst + 5qrst = 11qrst
11qrst + 4qrsty + qrsty = sqrt(y + 1)

Combine like terms: 4qrsty + qrsty = 5qrsty
11qrst + 5qrsty = sqrt(y + 1)

Reorder the terms:
11qrst + 5qrsty = qrst(1 + y)
11qrst + 5qrsty = (1 * qrst + y * qrst)
11qrst + 5qrsty = (1qrst + qrsty)

Solving
11qrst + 5qrsty = 1qrst + qrsty

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '-1qrst' to each side of the equation.
11qrst + -1qrst + 5qrsty = 1qrst + -1qrst + qrsty

Combine like terms: 11qrst + -1qrst = 10qrst
10qrst + 5qrsty = 1qrst + -1qrst + qrsty

Combine like terms: 1qrst + -1qrst = 0
10qrst + 5qrsty = 0 + qrsty
10qrst + 5qrsty = qrsty

Add '-1qrsty' to each side of the equation.
10qrst + 5qrsty + -1qrsty = qrsty + -1qrsty

Combine like terms: 5qrsty + -1qrsty = 4qrsty
10qrst + 4qrsty = qrsty + -1qrsty

Combine like terms: qrsty + -1qrsty = 0
10qrst + 4qrsty = 0

Factor out the Greatest Common Factor (GCF), '2qrst'.
2qrst(5 + 2y) = 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 '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Add '-2y' to each side of the equation. 2y + -2y = -5 + -2y Combine like terms: 2y + -2y = 0 0 = -5 + -2y Simplifying 0 = -5 + -2y 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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