25v^2+20v-4=0

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Solution for 25v^2+20v-4=0 equation: 


Simplifying
25v2 + 20v + -4 = 0

Reorder the terms:
-4 + 20v + 25v2 = 0

Solving
-4 + 20v + 25v2 = 0

Solving for variable 'v'.

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

Divide each side by '25'.
-0.16 + 0.8v + v2 = 0

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + 0.8v + 0.16 + v2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + 0.8v + v2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + 0.8v + v2 = 0 + 0.16
0.8v + v2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
0.8v + v2 = 0.16

The v term is 0.8v.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8v + 0.16 + v2 = 0.16 + 0.16

Reorder the terms:
0.16 + 0.8v + v2 = 0.16 + 0.16

Combine like terms: 0.16 + 0.16 = 0.32
0.16 + 0.8v + v2 = 0.32

Factor a perfect square on the left side:
(v + 0.4)(v + 0.4) = 0.32

Calculate the square root of the right side: 0.565685425

Break this problem into two subproblems by setting 
(v + 0.4) equal to 0.565685425 and -0.565685425.


Subproblem 1
v + 0.4 = 0.565685425

Simplifying
v + 0.4 = 0.565685425

Reorder the terms:
0.4 + v = 0.565685425

Solving
0.4 + v = 0.565685425

Solving for variable 'v'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + v = 0.565685425 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + v = 0.565685425 + -0.4
v = 0.565685425 + -0.4

Combine like terms: 0.565685425 + -0.4 = 0.165685425
v = 0.165685425

Simplifying
v = 0.165685425


Subproblem 2
v + 0.4 = -0.565685425

Simplifying
v + 0.4 = -0.565685425

Reorder the terms:
0.4 + v = -0.565685425

Solving
0.4 + v = -0.565685425

Solving for variable 'v'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + v = -0.565685425 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + v = -0.565685425 + -0.4
v = -0.565685425 + -0.4

Combine like terms: -0.565685425 + -0.4 = -0.965685425
v = -0.965685425

Simplifying
v = -0.965685425


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.165685425, -0.965685425}

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