(-3v^2+5v-4)+(2v^2+6v+7)=

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Solution for (-3v^2+5v-4)+(2v^2+6v+7)= equation:


Simplifying
(-3v2 + 5v + -4) + (2v2 + 6v + 7) = 0

Reorder the terms:
(-4 + 5v + -3v2) + (2v2 + 6v + 7) = 0

Remove parenthesis around (-4 + 5v + -3v2)
-4 + 5v + -3v2 + (2v2 + 6v + 7) = 0

Reorder the terms:
-4 + 5v + -3v2 + (7 + 6v + 2v2) = 0

Remove parenthesis around (7 + 6v + 2v2)
-4 + 5v + -3v2 + 7 + 6v + 2v2 = 0

Reorder the terms:
-4 + 7 + 5v + 6v + -3v2 + 2v2 = 0

Combine like terms: -4 + 7 = 3
3 + 5v + 6v + -3v2 + 2v2 = 0

Combine like terms: 5v + 6v = 11v
3 + 11v + -3v2 + 2v2 = 0

Combine like terms: -3v2 + 2v2 = -1v2
3 + 11v + -1v2 = 0

Solving
3 + 11v + -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'.
-3 + -11v + v2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -11v + 3 + v2 = 0 + 3

Reorder the terms:
-3 + 3 + -11v + v2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -11v + v2 = 0 + 3
-11v + v2 = 0 + 3

Combine like terms: 0 + 3 = 3
-11v + v2 = 3

The v term is -11v.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11v + 30.25 + v2 = 3 + 30.25

Reorder the terms:
30.25 + -11v + v2 = 3 + 30.25

Combine like terms: 3 + 30.25 = 33.25
30.25 + -11v + v2 = 33.25

Factor a perfect square on the left side:
(v + -5.5)(v + -5.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(v + -5.5) equal to 5.766281297 and -5.766281297.

Subproblem 1

v + -5.5 = 5.766281297 Simplifying v + -5.5 = 5.766281297 Reorder the terms: -5.5 + v = 5.766281297 Solving -5.5 + v = 5.766281297 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = 5.766281297 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = 5.766281297 + 5.5 v = 5.766281297 + 5.5 Combine like terms: 5.766281297 + 5.5 = 11.266281297 v = 11.266281297 Simplifying v = 11.266281297

Subproblem 2

v + -5.5 = -5.766281297 Simplifying v + -5.5 = -5.766281297 Reorder the terms: -5.5 + v = -5.766281297 Solving -5.5 + v = -5.766281297 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = -5.766281297 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = -5.766281297 + 5.5 v = -5.766281297 + 5.5 Combine like terms: -5.766281297 + 5.5 = -0.266281297 v = -0.266281297 Simplifying v = -0.266281297

Solution

The solution to the problem is based on the solutions from the subproblems. v = {11.266281297, -0.266281297}

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