v^2-20v+85=0

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Solution for v^2-20v+85=0 equation: 


Simplifying
v2 + -20v + 85 = 0

Reorder the terms:
85 + -20v + v2 = 0

Solving
85 + -20v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-85' to each side of the equation.
85 + -20v + -85 + v2 = 0 + -85

Reorder the terms:
85 + -85 + -20v + v2 = 0 + -85

Combine like terms: 85 + -85 = 0
0 + -20v + v2 = 0 + -85
-20v + v2 = 0 + -85

Combine like terms: 0 + -85 = -85
-20v + v2 = -85

The v term is -20v.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20v + 100 + v2 = -85 + 100

Reorder the terms:
100 + -20v + v2 = -85 + 100

Combine like terms: -85 + 100 = 15
100 + -20v + v2 = 15

Factor a perfect square on the left side:
(v + -10)(v + -10) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(v + -10) equal to 3.872983346 and -3.872983346.


Subproblem 1
v + -10 = 3.872983346

Simplifying
v + -10 = 3.872983346

Reorder the terms:
-10 + v = 3.872983346

Solving
-10 + v = 3.872983346

Solving for variable 'v'.

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

Add '10' to each side of the equation.
-10 + 10 + v = 3.872983346 + 10

Combine like terms: -10 + 10 = 0
0 + v = 3.872983346 + 10
v = 3.872983346 + 10

Combine like terms: 3.872983346 + 10 = 13.872983346
v = 13.872983346

Simplifying
v = 13.872983346


Subproblem 2
v + -10 = -3.872983346

Simplifying
v + -10 = -3.872983346

Reorder the terms:
-10 + v = -3.872983346

Solving
-10 + v = -3.872983346

Solving for variable 'v'.

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

Add '10' to each side of the equation.
-10 + 10 + v = -3.872983346 + 10

Combine like terms: -10 + 10 = 0
0 + v = -3.872983346 + 10
v = -3.872983346 + 10

Combine like terms: -3.872983346 + 10 = 6.127016654
v = 6.127016654

Simplifying
v = 6.127016654


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {13.872983346, 6.127016654}

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