(-2v^2+3v-1)+(4v^2+7v+5)=

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Solution for (-2v^2+3v-1)+(4v^2+7v+5)= equation: 


Simplifying
(-2v2 + 3v + -1) + (4v2 + 7v + 5) = 0

Reorder the terms:
(-1 + 3v + -2v2) + (4v2 + 7v + 5) = 0

Remove parenthesis around (-1 + 3v + -2v2)
-1 + 3v + -2v2 + (4v2 + 7v + 5) = 0

Reorder the terms:
-1 + 3v + -2v2 + (5 + 7v + 4v2) = 0

Remove parenthesis around (5 + 7v + 4v2)
-1 + 3v + -2v2 + 5 + 7v + 4v2 = 0

Reorder the terms:
-1 + 5 + 3v + 7v + -2v2 + 4v2 = 0

Combine like terms: -1 + 5 = 4
4 + 3v + 7v + -2v2 + 4v2 = 0

Combine like terms: 3v + 7v = 10v
4 + 10v + -2v2 + 4v2 = 0

Combine like terms: -2v2 + 4v2 = 2v2
4 + 10v + 2v2 = 0

Solving
4 + 10v + 2v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 5v + v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 5v + v2)' equal to zero and attempt to solve:

Simplifying
2 + 5v + v2 = 0

Solving
2 + 5v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5v + -2 + v2 = 0 + -2

Reorder the terms:
2 + -2 + 5v + v2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5v + v2 = 0 + -2
5v + v2 = 0 + -2

Combine like terms: 0 + -2 = -2
5v + v2 = -2

The v term is 5v.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5v + 6.25 + v2 = -2 + 6.25

Reorder the terms:
6.25 + 5v + v2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + 5v + v2 = 4.25

Factor a perfect square on the left side:
(v + 2.5)(v + 2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(v + 2.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
v + 2.5 = 2.061552813

Simplifying
v + 2.5 = 2.061552813

Reorder the terms:
2.5 + v = 2.061552813

Solving
2.5 + v = 2.061552813

Solving for variable 'v'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + v = 2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + v = 2.061552813 + -2.5
v = 2.061552813 + -2.5

Combine like terms: 2.061552813 + -2.5 = -0.438447187
v = -0.438447187

Simplifying
v = -0.438447187


Subproblem 2
v + 2.5 = -2.061552813

Simplifying
v + 2.5 = -2.061552813

Reorder the terms:
2.5 + v = -2.061552813

Solving
2.5 + v = -2.061552813

Solving for variable 'v'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + v = -2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + v = -2.061552813 + -2.5
v = -2.061552813 + -2.5

Combine like terms: -2.061552813 + -2.5 = -4.561552813
v = -4.561552813

Simplifying
v = -4.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.438447187, -4.561552813}
Solution
v = {-0.438447187, -4.561552813}

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