v^2-10v-6=0

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Solution for v^2-10v-6=0 equation: 


Simplifying
v2 + -10v + -6 = 0

Reorder the terms:
-6 + -10v + v2 = 0

Solving
-6 + -10v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -10v + 6 + v2 = 0 + 6

Reorder the terms:
-6 + 6 + -10v + v2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -10v + v2 = 0 + 6
-10v + v2 = 0 + 6

Combine like terms: 0 + 6 = 6
-10v + v2 = 6

The v term is -10v.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10v + 25 + v2 = 6 + 25

Reorder the terms:
25 + -10v + v2 = 6 + 25

Combine like terms: 6 + 25 = 31
25 + -10v + v2 = 31

Factor a perfect square on the left side:
(v + -5)(v + -5) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(v + -5) equal to 5.567764363 and -5.567764363.


Subproblem 1
v + -5 = 5.567764363

Simplifying
v + -5 = 5.567764363

Reorder the terms:
-5 + v = 5.567764363

Solving
-5 + v = 5.567764363

Solving for variable 'v'.

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

Add '5' to each side of the equation.
-5 + 5 + v = 5.567764363 + 5

Combine like terms: -5 + 5 = 0
0 + v = 5.567764363 + 5
v = 5.567764363 + 5

Combine like terms: 5.567764363 + 5 = 10.567764363
v = 10.567764363

Simplifying
v = 10.567764363


Subproblem 2
v + -5 = -5.567764363

Simplifying
v + -5 = -5.567764363

Reorder the terms:
-5 + v = -5.567764363

Solving
-5 + v = -5.567764363

Solving for variable 'v'.

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

Add '5' to each side of the equation.
-5 + 5 + v = -5.567764363 + 5

Combine like terms: -5 + 5 = 0
0 + v = -5.567764363 + 5
v = -5.567764363 + 5

Combine like terms: -5.567764363 + 5 = -0.567764363
v = -0.567764363

Simplifying
v = -0.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {10.567764363, -0.567764363}

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