v^2+10v-17=0

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Solution for v^2+10v-17=0 equation: 


Simplifying
v2 + 10v + -17 = 0

Reorder the terms:
-17 + 10v + v2 = 0

Solving
-17 + 10v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 10v + 17 + v2 = 0 + 17

Reorder the terms:
-17 + 17 + 10v + v2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 10v + v2 = 0 + 17
10v + v2 = 0 + 17

Combine like terms: 0 + 17 = 17
10v + v2 = 17

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 = 17 + 25

Reorder the terms:
25 + 10v + v2 = 17 + 25

Combine like terms: 17 + 25 = 42
25 + 10v + v2 = 42

Factor a perfect square on the left side:
(v + 5)(v + 5) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(v + 5) equal to 6.480740698 and -6.480740698.


Subproblem 1
v + 5 = 6.480740698

Simplifying
v + 5 = 6.480740698

Reorder the terms:
5 + v = 6.480740698

Solving
5 + v = 6.480740698

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 = 6.480740698 + -5

Combine like terms: 5 + -5 = 0
0 + v = 6.480740698 + -5
v = 6.480740698 + -5

Combine like terms: 6.480740698 + -5 = 1.480740698
v = 1.480740698

Simplifying
v = 1.480740698


Subproblem 2
v + 5 = -6.480740698

Simplifying
v + 5 = -6.480740698

Reorder the terms:
5 + v = -6.480740698

Solving
5 + v = -6.480740698

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 = -6.480740698 + -5

Combine like terms: 5 + -5 = 0
0 + v = -6.480740698 + -5
v = -6.480740698 + -5

Combine like terms: -6.480740698 + -5 = -11.480740698
v = -11.480740698

Simplifying
v = -11.480740698


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.480740698, -11.480740698}

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