sqrt(6x+13)=sqrt(8x+3)

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Solution for sqrt(6x+13)=sqrt(8x+3) equation:


Simplifying
sqrt(6x + 13) = sqrt(8x + 3)

Reorder the terms:
qrst(13 + 6x) = sqrt(8x + 3)
(13 * qrst + 6x * qrst) = sqrt(8x + 3)
(13qrst + 6qrstx) = sqrt(8x + 3)

Reorder the terms:
13qrst + 6qrstx = qrst(3 + 8x)
13qrst + 6qrstx = (3 * qrst + 8x * qrst)
13qrst + 6qrstx = (3qrst + 8qrstx)

Solving
13qrst + 6qrstx = 3qrst + 8qrstx

Solving for variable 'q'.

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

Add '-3qrst' to each side of the equation.
13qrst + -3qrst + 6qrstx = 3qrst + -3qrst + 8qrstx

Combine like terms: 13qrst + -3qrst = 10qrst
10qrst + 6qrstx = 3qrst + -3qrst + 8qrstx

Combine like terms: 3qrst + -3qrst = 0
10qrst + 6qrstx = 0 + 8qrstx
10qrst + 6qrstx = 8qrstx

Add '-8qrstx' to each side of the equation.
10qrst + 6qrstx + -8qrstx = 8qrstx + -8qrstx

Combine like terms: 6qrstx + -8qrstx = -2qrstx
10qrst + -2qrstx = 8qrstx + -8qrstx

Combine like terms: 8qrstx + -8qrstx = 0
10qrst + -2qrstx = 0

Factor out the Greatest Common Factor (GCF), '2qrst'.
2qrst(5 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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