((-5v^2)+6v-3)+(4v^2)+v+2=0

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Solution for ((-5v^2)+6v-3)+(4v^2)+v+2=0 equation:


Simplifying
((-5v2) + 6v + -3) + (4v2) + v + 2 = 0

Reorder the terms:
(-3 + 6v + (-5v2)) + (4v2) + v + 2 = 0

Remove parenthesis around (-3 + 6v + (-5v2))
-3 + 6v + (-5v2) + (4v2) + v + 2 = 0

Reorder the terms:
-3 + 2 + 6v + v + (-5v2) + (4v2) = 0

Combine like terms: -3 + 2 = -1
-1 + 6v + v + (-5v2) + (4v2) = 0

Combine like terms: 6v + v = 7v
-1 + 7v + (-5v2) + (4v2) = 0

Combine like terms: (-5v2) + (4v2) = -1v2
-1 + 7v + -1v2 = 0

Solving
-1 + 7v + -1v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1 + -7v + v2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -7v + -1 + v2 = 0 + -1

Reorder the terms:
1 + -1 + -7v + v2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7v + v2 = 0 + -1
-7v + v2 = 0 + -1

Combine like terms: 0 + -1 = -1
-7v + v2 = -1

The v term is -7v.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7v + 12.25 + v2 = -1 + 12.25

Reorder the terms:
12.25 + -7v + v2 = -1 + 12.25

Combine like terms: -1 + 12.25 = 11.25
12.25 + -7v + v2 = 11.25

Factor a perfect square on the left side:
(v + -3.5)(v + -3.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(v + -3.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

v + -3.5 = 3.354101966 Simplifying v + -3.5 = 3.354101966 Reorder the terms: -3.5 + v = 3.354101966 Solving -3.5 + v = 3.354101966 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = 3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = 3.354101966 + 3.5 v = 3.354101966 + 3.5 Combine like terms: 3.354101966 + 3.5 = 6.854101966 v = 6.854101966 Simplifying v = 6.854101966

Subproblem 2

v + -3.5 = -3.354101966 Simplifying v + -3.5 = -3.354101966 Reorder the terms: -3.5 + v = -3.354101966 Solving -3.5 + v = -3.354101966 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = -3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = -3.354101966 + 3.5 v = -3.354101966 + 3.5 Combine like terms: -3.354101966 + 3.5 = 0.145898034 v = 0.145898034 Simplifying v = 0.145898034

Solution

The solution to the problem is based on the solutions from the subproblems. v = {6.854101966, 0.145898034}

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