2v^2+7v-7=0

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Solution for 2v^2+7v-7=0 equation: 


Simplifying
2v2 + 7v + -7 = 0

Reorder the terms:
-7 + 7v + 2v2 = 0

Solving
-7 + 7v + 2v2 = 0

Solving for variable 'v'.

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

Divide each side by '2'.
-3.5 + 3.5v + v2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 3.5v + 3.5 + v2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 3.5v + v2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 3.5v + v2 = 0 + 3.5
3.5v + v2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
3.5v + v2 = 3.5

The v term is 3.5v.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5v + 3.0625 + v2 = 3.5 + 3.0625

Reorder the terms:
3.0625 + 3.5v + v2 = 3.5 + 3.0625

Combine like terms: 3.5 + 3.0625 = 6.5625
3.0625 + 3.5v + v2 = 6.5625

Factor a perfect square on the left side:
(v + 1.75)(v + 1.75) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(v + 1.75) equal to 2.561737691 and -2.561737691.


Subproblem 1
v + 1.75 = 2.561737691

Simplifying
v + 1.75 = 2.561737691

Reorder the terms:
1.75 + v = 2.561737691

Solving
1.75 + v = 2.561737691

Solving for variable 'v'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + v = 2.561737691 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + v = 2.561737691 + -1.75
v = 2.561737691 + -1.75

Combine like terms: 2.561737691 + -1.75 = 0.811737691
v = 0.811737691

Simplifying
v = 0.811737691


Subproblem 2
v + 1.75 = -2.561737691

Simplifying
v + 1.75 = -2.561737691

Reorder the terms:
1.75 + v = -2.561737691

Solving
1.75 + v = -2.561737691

Solving for variable 'v'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + v = -2.561737691 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + v = -2.561737691 + -1.75
v = -2.561737691 + -1.75

Combine like terms: -2.561737691 + -1.75 = -4.311737691
v = -4.311737691

Simplifying
v = -4.311737691


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.811737691, -4.311737691}

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