6v^2-25v+20=0

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Solution for 6v^2-25v+20=0 equation: 


Simplifying
6v2 + -25v + 20 = 0

Reorder the terms:
20 + -25v + 6v2 = 0

Solving
20 + -25v + 6v2 = 0

Solving for variable 'v'.

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

Divide each side by '6'.
3.333333333 + -4.166666667v + v2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -4.166666667v + -3.333333333 + v2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -4.166666667v + v2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -4.166666667v + v2 = 0 + -3.333333333
-4.166666667v + v2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-4.166666667v + v2 = -3.333333333

The v term is -4.166666667v.  Take half its coefficient (-2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
-4.166666667v + 4.340277781 + v2 = -3.333333333 + 4.340277781

Reorder the terms:
4.340277781 + -4.166666667v + v2 = -3.333333333 + 4.340277781

Combine like terms: -3.333333333 + 4.340277781 = 1.006944448
4.340277781 + -4.166666667v + v2 = 1.006944448

Factor a perfect square on the left side:
(v + -2.083333334)(v + -2.083333334) = 1.006944448

Calculate the square root of the right side: 1.003466217

Break this problem into two subproblems by setting 
(v + -2.083333334) equal to 1.003466217 and -1.003466217.


Subproblem 1
v + -2.083333334 = 1.003466217

Simplifying
v + -2.083333334 = 1.003466217

Reorder the terms:
-2.083333334 + v = 1.003466217

Solving
-2.083333334 + v = 1.003466217

Solving for variable 'v'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + v = 1.003466217 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + v = 1.003466217 + 2.083333334
v = 1.003466217 + 2.083333334

Combine like terms: 1.003466217 + 2.083333334 = 3.086799551
v = 3.086799551

Simplifying
v = 3.086799551


Subproblem 2
v + -2.083333334 = -1.003466217

Simplifying
v + -2.083333334 = -1.003466217

Reorder the terms:
-2.083333334 + v = -1.003466217

Solving
-2.083333334 + v = -1.003466217

Solving for variable 'v'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + v = -1.003466217 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + v = -1.003466217 + 2.083333334
v = -1.003466217 + 2.083333334

Combine like terms: -1.003466217 + 2.083333334 = 1.079867117
v = 1.079867117

Simplifying
v = 1.079867117


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {3.086799551, 1.079867117}

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