v^2-v=11

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Solution for v^2-v=11 equation:


Simplifying
v2 + -1v = 11

Reorder the terms:
-1v + v2 = 11

Solving
-1v + v2 = 11

Solving for variable 'v'.

Reorder the terms:
-11 + -1v + v2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -1v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -1v + 11 + v2 = 0 + 11

Reorder the terms:
-11 + 11 + -1v + v2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1v + v2 = 0 + 11
-1v + v2 = 0 + 11

Combine like terms: 0 + 11 = 11
-1v + v2 = 11

The v term is -1v.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1v + 0.25 + v2 = 11 + 0.25

Reorder the terms:
0.25 + -1v + v2 = 11 + 0.25

Combine like terms: 11 + 0.25 = 11.25
0.25 + -1v + v2 = 11.25

Factor a perfect square on the left side:
(v + -0.5)(v + -0.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(v + -0.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

v + -0.5 = 3.354101966 Simplifying v + -0.5 = 3.354101966 Reorder the terms: -0.5 + v = 3.354101966 Solving -0.5 + v = 3.354101966 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 3.354101966 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 3.354101966 + 0.5 v = 3.354101966 + 0.5 Combine like terms: 3.354101966 + 0.5 = 3.854101966 v = 3.854101966 Simplifying v = 3.854101966

Subproblem 2

v + -0.5 = -3.354101966 Simplifying v + -0.5 = -3.354101966 Reorder the terms: -0.5 + v = -3.354101966 Solving -0.5 + v = -3.354101966 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -3.354101966 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -3.354101966 + 0.5 v = -3.354101966 + 0.5 Combine like terms: -3.354101966 + 0.5 = -2.854101966 v = -2.854101966 Simplifying v = -2.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. v = {3.854101966, -2.854101966}

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