5*sqrt(x^3+1)=2*sqrt(x^2+2)

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Solution for 5*sqrt(x^3+1)=2*sqrt(x^2+2) equation: 


Simplifying
5sqrt(x3 + 1) = 2sqrt(x2 + 2)

Reorder the terms:
5qrst(1 + x3) = 2sqrt(x2 + 2)
(1 * 5qrst + x3 * 5qrst) = 2sqrt(x2 + 2)
(5qrst + 5qrstx3) = 2sqrt(x2 + 2)

Reorder the terms:
5qrst + 5qrstx3 = 2qrst(2 + x2)
5qrst + 5qrstx3 = (2 * 2qrst + x2 * 2qrst)
5qrst + 5qrstx3 = (4qrst + 2qrstx2)

Solving
5qrst + 5qrstx3 = 4qrst + 2qrstx2

Solving for variable 'q'.

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

Add '-4qrst' to each side of the equation.
5qrst + -4qrst + 5qrstx3 = 4qrst + -4qrst + 2qrstx2

Combine like terms: 5qrst + -4qrst = 1qrst
1qrst + 5qrstx3 = 4qrst + -4qrst + 2qrstx2

Combine like terms: 4qrst + -4qrst = 0
1qrst + 5qrstx3 = 0 + 2qrstx2
1qrst + 5qrstx3 = 2qrstx2

Add '-2qrstx2' to each side of the equation.
1qrst + -2qrstx2 + 5qrstx3 = 2qrstx2 + -2qrstx2

Combine like terms: 2qrstx2 + -2qrstx2 = 0
1qrst + -2qrstx2 + 5qrstx3 = 0

Factor out the Greatest Common Factor (GCF), 'qrst'.
qrst(1 + -2x2 + 5x3) = 0


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 '(1 + -2x2 + 5x3)' equal to zero and attempt to solve:

Simplifying
1 + -2x2 + 5x3 = 0

Solving
1 + -2x2 + 5x3 = 0

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

Add '-1' to each side of the equation.
1 + -2x2 + -1 + 5x3 = 0 + -1

Reorder the terms:
1 + -1 + -2x2 + 5x3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 + 5x3 = 0 + -1
-2x2 + 5x3 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 + 5x3 = -1

Add '2x2' to each side of the equation.
-2x2 + 2x2 + 5x3 = -1 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + 5x3 = -1 + 2x2
5x3 = -1 + 2x2

Add '-5x3' to each side of the equation.
5x3 + -5x3 = -1 + 2x2 + -5x3

Combine like terms: 5x3 + -5x3 = 0
0 = -1 + 2x2 + -5x3

Simplifying
0 = -1 + 2x2 + -5x3

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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