4v^2-22v-35=0

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Solution for 4v^2-22v-35=0 equation: 


Simplifying
4v2 + -22v + -35 = 0

Reorder the terms:
-35 + -22v + 4v2 = 0

Solving
-35 + -22v + 4v2 = 0

Solving for variable 'v'.

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

Divide each side by '4'.
-8.75 + -5.5v + v2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + -5.5v + 8.75 + v2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + -5.5v + v2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + -5.5v + v2 = 0 + 8.75
-5.5v + v2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
-5.5v + v2 = 8.75

The v term is -5.5v.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5v + 7.5625 + v2 = 8.75 + 7.5625

Reorder the terms:
7.5625 + -5.5v + v2 = 8.75 + 7.5625

Combine like terms: 8.75 + 7.5625 = 16.3125
7.5625 + -5.5v + v2 = 16.3125

Factor a perfect square on the left side:
(v + -2.75)(v + -2.75) = 16.3125

Calculate the square root of the right side: 4.038873605

Break this problem into two subproblems by setting 
(v + -2.75) equal to 4.038873605 and -4.038873605.


Subproblem 1
v + -2.75 = 4.038873605

Simplifying
v + -2.75 = 4.038873605

Reorder the terms:
-2.75 + v = 4.038873605

Solving
-2.75 + v = 4.038873605

Solving for variable 'v'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + v = 4.038873605 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + v = 4.038873605 + 2.75
v = 4.038873605 + 2.75

Combine like terms: 4.038873605 + 2.75 = 6.788873605
v = 6.788873605

Simplifying
v = 6.788873605


Subproblem 2
v + -2.75 = -4.038873605

Simplifying
v + -2.75 = -4.038873605

Reorder the terms:
-2.75 + v = -4.038873605

Solving
-2.75 + v = -4.038873605

Solving for variable 'v'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + v = -4.038873605 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + v = -4.038873605 + 2.75
v = -4.038873605 + 2.75

Combine like terms: -4.038873605 + 2.75 = -1.288873605
v = -1.288873605

Simplifying
v = -1.288873605


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {6.788873605, -1.288873605}

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