Sqrt[11+2x]=Sqrt[14+3x]

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Solution for Sqrt[11+2x]=Sqrt[14+3x] equation:


Simplifying
Sqrt[11 + 2x] = Sqrt[14 + 3x]
[11 * qrtS + 2x * qrtS] = Sqrt[14 + 3x]
[11qrtS + 2qrtxS] = Sqrt[14 + 3x]
11qrtS + 2qrtxS = [14 * qrtS + 3x * qrtS]
11qrtS + 2qrtxS = [14qrtS + 3qrtxS]

Solving
11qrtS + 2qrtxS = 14qrtS + 3qrtxS

Solving for variable 'q'.

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

Add '-14qrtS' to each side of the equation.
11qrtS + -14qrtS + 2qrtxS = 14qrtS + -14qrtS + 3qrtxS

Combine like terms: 11qrtS + -14qrtS = -3qrtS
-3qrtS + 2qrtxS = 14qrtS + -14qrtS + 3qrtxS

Combine like terms: 14qrtS + -14qrtS = 0
-3qrtS + 2qrtxS = 0 + 3qrtxS
-3qrtS + 2qrtxS = 3qrtxS

Add '-3qrtxS' to each side of the equation.
-3qrtS + 2qrtxS + -3qrtxS = 3qrtxS + -3qrtxS

Combine like terms: 2qrtxS + -3qrtxS = -1qrtxS
-3qrtS + -1qrtxS = 3qrtxS + -3qrtxS

Combine like terms: 3qrtxS + -3qrtxS = 0
-3qrtS + -1qrtxS = 0

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

Ignore the factor -1.

Subproblem 1

Set the factor 'qrtS' equal to zero and attempt to solve: Simplifying qrtS = 0 Solving qrtS = 0 Move all terms containing q to the left, all other terms to the right. Simplifying qrtS = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x 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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