4v^2-v-2=0

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Solution for 4v^2-v-2=0 equation: 


Simplifying
4v2 + -1v + -2 = 0

Reorder the terms:
-2 + -1v + 4v2 = 0

Solving
-2 + -1v + 4v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-0.5 + -0.25v + v2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.25v + 0.5 + v2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.25v + v2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.25v + v2 = 0 + 0.5
-0.25v + v2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.25v + v2 = 0.5

The v term is -0.25v.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25v + 0.015625 + v2 = 0.5 + 0.015625

Reorder the terms:
0.015625 + -0.25v + v2 = 0.5 + 0.015625

Combine like terms: 0.5 + 0.015625 = 0.515625
0.015625 + -0.25v + v2 = 0.515625

Factor a perfect square on the left side:
(v + -0.125)(v + -0.125) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(v + -0.125) equal to 0.718070331 and -0.718070331.


Subproblem 1
v + -0.125 = 0.718070331

Simplifying
v + -0.125 = 0.718070331

Reorder the terms:
-0.125 + v = 0.718070331

Solving
-0.125 + v = 0.718070331

Solving for variable 'v'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + v = 0.718070331 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + v = 0.718070331 + 0.125
v = 0.718070331 + 0.125

Combine like terms: 0.718070331 + 0.125 = 0.843070331
v = 0.843070331

Simplifying
v = 0.843070331


Subproblem 2
v + -0.125 = -0.718070331

Simplifying
v + -0.125 = -0.718070331

Reorder the terms:
-0.125 + v = -0.718070331

Solving
-0.125 + v = -0.718070331

Solving for variable 'v'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + v = -0.718070331 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + v = -0.718070331 + 0.125
v = -0.718070331 + 0.125

Combine like terms: -0.718070331 + 0.125 = -0.593070331
v = -0.593070331

Simplifying
v = -0.593070331


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.843070331, -0.593070331}

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