v^2+10v-21=0

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Solution for v^2+10v-21=0 equation: 


Simplifying
v2 + 10v + -21 = 0

Reorder the terms:
-21 + 10v + v2 = 0

Solving
-21 + 10v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 10v + 21 + v2 = 0 + 21

Reorder the terms:
-21 + 21 + 10v + v2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 10v + v2 = 0 + 21
10v + v2 = 0 + 21

Combine like terms: 0 + 21 = 21
10v + v2 = 21

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 = 21 + 25

Reorder the terms:
25 + 10v + v2 = 21 + 25

Combine like terms: 21 + 25 = 46
25 + 10v + v2 = 46

Factor a perfect square on the left side:
(v + 5)(v + 5) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(v + 5) equal to 6.782329983 and -6.782329983.


Subproblem 1
v + 5 = 6.782329983

Simplifying
v + 5 = 6.782329983

Reorder the terms:
5 + v = 6.782329983

Solving
5 + v = 6.782329983

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 = 6.782329983 + -5

Combine like terms: 5 + -5 = 0
0 + v = 6.782329983 + -5
v = 6.782329983 + -5

Combine like terms: 6.782329983 + -5 = 1.782329983
v = 1.782329983

Simplifying
v = 1.782329983


Subproblem 2
v + 5 = -6.782329983

Simplifying
v + 5 = -6.782329983

Reorder the terms:
5 + v = -6.782329983

Solving
5 + v = -6.782329983

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 = -6.782329983 + -5

Combine like terms: 5 + -5 = 0
0 + v = -6.782329983 + -5
v = -6.782329983 + -5

Combine like terms: -6.782329983 + -5 = -11.782329983
v = -11.782329983

Simplifying
v = -11.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.782329983, -11.782329983}

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