v^2+v-8=0

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Solution for v^2+v-8=0 equation: 


Simplifying
v2 + v + -8 = 0

Reorder the terms:
-8 + v + v2 = 0

Solving
-8 + v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + v + 8 + v2 = 0 + 8

Reorder the terms:
-8 + 8 + v + v2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + v + v2 = 0 + 8
v + v2 = 0 + 8

Combine like terms: 0 + 8 = 8
v + v2 = 8

The v term is v.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
v + 0.25 + v2 = 8 + 0.25

Reorder the terms:
0.25 + v + v2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + v + v2 = 8.25

Factor a perfect square on the left side:
(v + 0.5)(v + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(v + 0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
v + 0.5 = 2.872281323

Simplifying
v + 0.5 = 2.872281323

Reorder the terms:
0.5 + v = 2.872281323

Solving
0.5 + v = 2.872281323

Solving for variable 'v'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + v = 2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + v = 2.872281323 + -0.5
v = 2.872281323 + -0.5

Combine like terms: 2.872281323 + -0.5 = 2.372281323
v = 2.372281323

Simplifying
v = 2.372281323


Subproblem 2
v + 0.5 = -2.872281323

Simplifying
v + 0.5 = -2.872281323

Reorder the terms:
0.5 + v = -2.872281323

Solving
0.5 + v = -2.872281323

Solving for variable 'v'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + v = -2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + v = -2.872281323 + -0.5
v = -2.872281323 + -0.5

Combine like terms: -2.872281323 + -0.5 = -3.372281323
v = -3.372281323

Simplifying
v = -3.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.372281323, -3.372281323}

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