7v^2-42=36v

Solution for 7v^2-42=36v equation:

Simplifying
7v2 + -42 = 36v

Reorder the terms:
-42 + 7v2 = 36v

Solving
-42 + 7v2 = 36v

Solving for variable 'v'.

Reorder the terms:
-42 + -36v + 7v2 = 36v + -36v

Combine like terms: 36v + -36v = 0
-42 + -36v + 7v2 = 0

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

Divide each side by '7'.
-6 + -5.142857143v + v2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -5.142857143v + 6 + v2 = 0 + 6

Reorder the terms:
-6 + 6 + -5.142857143v + v2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5.142857143v + v2 = 0 + 6
-5.142857143v + v2 = 0 + 6

Combine like terms: 0 + 6 = 6
-5.142857143v + v2 = 6

The v term is -5.142857143v.  Take half its coefficient (-2.571428572).
Square it (6.612244901) and add it to both sides.

Add '6.612244901' to each side of the equation.
-5.142857143v + 6.612244901 + v2 = 6 + 6.612244901

Reorder the terms:
6.612244901 + -5.142857143v + v2 = 6 + 6.612244901

Combine like terms: 6 + 6.612244901 = 12.612244901
6.612244901 + -5.142857143v + v2 = 12.612244901

Factor a perfect square on the left side:
(v + -2.571428572)(v + -2.571428572) = 12.612244901

Calculate the square root of the right side: 3.551372256

Break this problem into two subproblems by setting 
(v + -2.571428572) equal to 3.551372256 and -3.551372256.

Subproblem 1
v + -2.571428572 = 3.551372256

Simplifying
v + -2.571428572 = 3.551372256

Reorder the terms:
-2.571428572 + v = 3.551372256

Solving
-2.571428572 + v = 3.551372256

Solving for variable 'v'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + v = 3.551372256 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + v = 3.551372256 + 2.571428572
v = 3.551372256 + 2.571428572

Combine like terms: 3.551372256 + 2.571428572 = 6.122800828
v = 6.122800828

Simplifying
v = 6.122800828

Subproblem 2
v + -2.571428572 = -3.551372256

Simplifying
v + -2.571428572 = -3.551372256

Reorder the terms:
-2.571428572 + v = -3.551372256

Solving
-2.571428572 + v = -3.551372256

Solving for variable 'v'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + v = -3.551372256 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + v = -3.551372256 + 2.571428572
v = -3.551372256 + 2.571428572

Combine like terms: -3.551372256 + 2.571428572 = -0.979943684
v = -0.979943684

Simplifying
v = -0.979943684

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {6.122800828, -0.979943684}