4v^2-5v-5=0

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Solution for 4v^2-5v-5=0 equation: 


Simplifying
4v2 + -5v + -5 = 0

Reorder the terms:
-5 + -5v + 4v2 = 0

Solving
-5 + -5v + 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'.
-1.25 + -1.25v + v2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.25v + 1.25 + v2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.25v + v2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.25v + v2 = 0 + 1.25
-1.25v + v2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.25v + v2 = 1.25

The v term is -1.25v.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25v + 0.390625 + v2 = 1.25 + 0.390625

Reorder the terms:
0.390625 + -1.25v + v2 = 1.25 + 0.390625

Combine like terms: 1.25 + 0.390625 = 1.640625
0.390625 + -1.25v + v2 = 1.640625

Factor a perfect square on the left side:
(v + -0.625)(v + -0.625) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(v + -0.625) equal to 1.280868846 and -1.280868846.


Subproblem 1
v + -0.625 = 1.280868846

Simplifying
v + -0.625 = 1.280868846

Reorder the terms:
-0.625 + v = 1.280868846

Solving
-0.625 + v = 1.280868846

Solving for variable 'v'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + v = 1.280868846 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + v = 1.280868846 + 0.625
v = 1.280868846 + 0.625

Combine like terms: 1.280868846 + 0.625 = 1.905868846
v = 1.905868846

Simplifying
v = 1.905868846


Subproblem 2
v + -0.625 = -1.280868846

Simplifying
v + -0.625 = -1.280868846

Reorder the terms:
-0.625 + v = -1.280868846

Solving
-0.625 + v = -1.280868846

Solving for variable 'v'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + v = -1.280868846 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + v = -1.280868846 + 0.625
v = -1.280868846 + 0.625

Combine like terms: -1.280868846 + 0.625 = -0.655868846
v = -0.655868846

Simplifying
v = -0.655868846


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.905868846, -0.655868846}

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