v^2-10v+7=0

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Solution for v^2-10v+7=0 equation: 


Simplifying
v2 + -10v + 7 = 0

Reorder the terms:
7 + -10v + v2 = 0

Solving
7 + -10v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -10v + -7 + v2 = 0 + -7

Reorder the terms:
7 + -7 + -10v + v2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -10v + v2 = 0 + -7
-10v + v2 = 0 + -7

Combine like terms: 0 + -7 = -7
-10v + v2 = -7

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 = -7 + 25

Reorder the terms:
25 + -10v + v2 = -7 + 25

Combine like terms: -7 + 25 = 18
25 + -10v + v2 = 18

Factor a perfect square on the left side:
(v + -5)(v + -5) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(v + -5) equal to 4.242640687 and -4.242640687.


Subproblem 1
v + -5 = 4.242640687

Simplifying
v + -5 = 4.242640687

Reorder the terms:
-5 + v = 4.242640687

Solving
-5 + v = 4.242640687

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 = 4.242640687 + 5

Combine like terms: -5 + 5 = 0
0 + v = 4.242640687 + 5
v = 4.242640687 + 5

Combine like terms: 4.242640687 + 5 = 9.242640687
v = 9.242640687

Simplifying
v = 9.242640687


Subproblem 2
v + -5 = -4.242640687

Simplifying
v + -5 = -4.242640687

Reorder the terms:
-5 + v = -4.242640687

Solving
-5 + v = -4.242640687

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 = -4.242640687 + 5

Combine like terms: -5 + 5 = 0
0 + v = -4.242640687 + 5
v = -4.242640687 + 5

Combine like terms: -4.242640687 + 5 = 0.757359313
v = 0.757359313

Simplifying
v = 0.757359313


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {9.242640687, 0.757359313}

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