v^2-22v-50=-7

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Solution for v^2-22v-50=-7 equation: 


Simplifying
v2 + -22v + -50 = -7

Reorder the terms:
-50 + -22v + v2 = -7

Solving
-50 + -22v + v2 = -7

Solving for variable 'v'.

Reorder the terms:
-50 + 7 + -22v + v2 = -7 + 7

Combine like terms: -50 + 7 = -43
-43 + -22v + v2 = -7 + 7

Combine like terms: -7 + 7 = 0
-43 + -22v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -22v + 43 + v2 = 0 + 43

Reorder the terms:
-43 + 43 + -22v + v2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -22v + v2 = 0 + 43
-22v + v2 = 0 + 43

Combine like terms: 0 + 43 = 43
-22v + v2 = 43

The v term is -22v.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22v + 121 + v2 = 43 + 121

Reorder the terms:
121 + -22v + v2 = 43 + 121

Combine like terms: 43 + 121 = 164
121 + -22v + v2 = 164

Factor a perfect square on the left side:
(v + -11)(v + -11) = 164

Calculate the square root of the right side: 12.806248475

Break this problem into two subproblems by setting 
(v + -11) equal to 12.806248475 and -12.806248475.


Subproblem 1
v + -11 = 12.806248475

Simplifying
v + -11 = 12.806248475

Reorder the terms:
-11 + v = 12.806248475

Solving
-11 + v = 12.806248475

Solving for variable 'v'.

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

Add '11' to each side of the equation.
-11 + 11 + v = 12.806248475 + 11

Combine like terms: -11 + 11 = 0
0 + v = 12.806248475 + 11
v = 12.806248475 + 11

Combine like terms: 12.806248475 + 11 = 23.806248475
v = 23.806248475

Simplifying
v = 23.806248475


Subproblem 2
v + -11 = -12.806248475

Simplifying
v + -11 = -12.806248475

Reorder the terms:
-11 + v = -12.806248475

Solving
-11 + v = -12.806248475

Solving for variable 'v'.

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

Add '11' to each side of the equation.
-11 + 11 + v = -12.806248475 + 11

Combine like terms: -11 + 11 = 0
0 + v = -12.806248475 + 11
v = -12.806248475 + 11

Combine like terms: -12.806248475 + 11 = -1.806248475
v = -1.806248475

Simplifying
v = -1.806248475


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {23.806248475, -1.806248475}

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