sqrt(4x+9)=3+sqrt(x)

Solution for sqrt(4x+9)=3+sqrt(x) equation:

Simplifying
sqrt(4x + 9) = 3 + sqrt(x)

Reorder the terms:
qrst(9 + 4x) = 3 + sqrt(x)
(9 * qrst + 4x * qrst) = 3 + sqrt(x)
(9qrst + 4qrstx) = 3 + sqrt(x)

Multiply qrst * x
9qrst + 4qrstx = 3 + qrstx

Solving
9qrst + 4qrstx = 3 + qrstx

Solving for variable 'q'.

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

Add '-1qrstx' to each side of the equation.
9qrst + 4qrstx + -1qrstx = 3 + qrstx + -1qrstx

Combine like terms: 4qrstx + -1qrstx = 3qrstx
9qrst + 3qrstx = 3 + qrstx + -1qrstx

Combine like terms: qrstx + -1qrstx = 0
9qrst + 3qrstx = 3 + 0
9qrst + 3qrstx = 3

Reorder the terms:
-3 + 9qrst + 3qrstx = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 9qrst + 3qrstx = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 3qrst + qrstx) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 3qrst + qrstx)' equal to zero and attempt to solve:

Simplifying
-1 + 3qrst + qrstx = 0

Solving
-1 + 3qrst + qrstx = 0

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

Add '1' to each side of the equation.
-1 + 3qrst + 1 + qrstx = 0 + 1

Reorder the terms:
-1 + 1 + 3qrst + qrstx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3qrst + qrstx = 0 + 1
3qrst + qrstx = 0 + 1

Combine like terms: 0 + 1 = 1
3qrst + qrstx = 1

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.