v^2+10v-15=0

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Solution for v^2+10v-15=0 equation: 


Simplifying
v2 + 10v + -15 = 0

Reorder the terms:
-15 + 10v + v2 = 0

Solving
-15 + 10v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 10v + 15 + v2 = 0 + 15

Reorder the terms:
-15 + 15 + 10v + v2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 10v + v2 = 0 + 15
10v + v2 = 0 + 15

Combine like terms: 0 + 15 = 15
10v + v2 = 15

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 = 15 + 25

Reorder the terms:
25 + 10v + v2 = 15 + 25

Combine like terms: 15 + 25 = 40
25 + 10v + v2 = 40

Factor a perfect square on the left side:
(v + 5)(v + 5) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(v + 5) equal to 6.32455532 and -6.32455532.


Subproblem 1
v + 5 = 6.32455532

Simplifying
v + 5 = 6.32455532

Reorder the terms:
5 + v = 6.32455532

Solving
5 + v = 6.32455532

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 = 6.32455532 + -5

Combine like terms: 5 + -5 = 0
0 + v = 6.32455532 + -5
v = 6.32455532 + -5

Combine like terms: 6.32455532 + -5 = 1.32455532
v = 1.32455532

Simplifying
v = 1.32455532


Subproblem 2
v + 5 = -6.32455532

Simplifying
v + 5 = -6.32455532

Reorder the terms:
5 + v = -6.32455532

Solving
5 + v = -6.32455532

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 = -6.32455532 + -5

Combine like terms: 5 + -5 = 0
0 + v = -6.32455532 + -5
v = -6.32455532 + -5

Combine like terms: -6.32455532 + -5 = -11.32455532
v = -11.32455532

Simplifying
v = -11.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.32455532, -11.32455532}

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