-6+8v=v^2

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Solution for -6+8v=v^2 equation: 


Simplifying
-6 + 8v = v2

Solving
-6 + 8v = v2

Solving for variable 'v'.

Combine like terms: v2 + -1v2 = 0
-6 + 8v + -1v2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -8v + v2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8v + -6 + v2 = 0 + -6

Reorder the terms:
6 + -6 + -8v + v2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8v + v2 = 0 + -6
-8v + v2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8v + v2 = -6

The v term is -8v.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8v + 16 + v2 = -6 + 16

Reorder the terms:
16 + -8v + v2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8v + v2 = 10

Factor a perfect square on the left side:
(v + -4)(v + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(v + -4) equal to 3.16227766 and -3.16227766.


Subproblem 1
v + -4 = 3.16227766

Simplifying
v + -4 = 3.16227766

Reorder the terms:
-4 + v = 3.16227766

Solving
-4 + v = 3.16227766

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = 3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + v = 3.16227766 + 4
v = 3.16227766 + 4

Combine like terms: 3.16227766 + 4 = 7.16227766
v = 7.16227766

Simplifying
v = 7.16227766


Subproblem 2
v + -4 = -3.16227766

Simplifying
v + -4 = -3.16227766

Reorder the terms:
-4 + v = -3.16227766

Solving
-4 + v = -3.16227766

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = -3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + v = -3.16227766 + 4
v = -3.16227766 + 4

Combine like terms: -3.16227766 + 4 = 0.83772234
v = 0.83772234

Simplifying
v = 0.83772234


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {7.16227766, 0.83772234}

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