-4v^2-34v-49=0

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Solution for -4v^2-34v-49=0 equation: 


Simplifying
-4v2 + -34v + -49 = 0

Reorder the terms:
-49 + -34v + -4v2 = 0

Solving
-49 + -34v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(49 + 34v + 4v2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(49 + 34v + 4v2)' equal to zero and attempt to solve:

Simplifying
49 + 34v + 4v2 = 0

Solving
49 + 34v + 4v2 = 0

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

Divide each side by '4'.
12.25 + 8.5v + v2 = 0

Move the constant term to the right:

Add '-12.25' to each side of the equation.
12.25 + 8.5v + -12.25 + v2 = 0 + -12.25

Reorder the terms:
12.25 + -12.25 + 8.5v + v2 = 0 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + 8.5v + v2 = 0 + -12.25
8.5v + v2 = 0 + -12.25

Combine like terms: 0 + -12.25 = -12.25
8.5v + v2 = -12.25

The v term is 8.5v.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5v + 18.0625 + v2 = -12.25 + 18.0625

Reorder the terms:
18.0625 + 8.5v + v2 = -12.25 + 18.0625

Combine like terms: -12.25 + 18.0625 = 5.8125
18.0625 + 8.5v + v2 = 5.8125

Factor a perfect square on the left side:
(v + 4.25)(v + 4.25) = 5.8125

Calculate the square root of the right side: 2.41091269

Break this problem into two subproblems by setting 
(v + 4.25) equal to 2.41091269 and -2.41091269.


Subproblem 1
v + 4.25 = 2.41091269

Simplifying
v + 4.25 = 2.41091269

Reorder the terms:
4.25 + v = 2.41091269

Solving
4.25 + v = 2.41091269

Solving for variable 'v'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + v = 2.41091269 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + v = 2.41091269 + -4.25
v = 2.41091269 + -4.25

Combine like terms: 2.41091269 + -4.25 = -1.83908731
v = -1.83908731

Simplifying
v = -1.83908731


Subproblem 2
v + 4.25 = -2.41091269

Simplifying
v + 4.25 = -2.41091269

Reorder the terms:
4.25 + v = -2.41091269

Solving
4.25 + v = -2.41091269

Solving for variable 'v'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + v = -2.41091269 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + v = -2.41091269 + -4.25
v = -2.41091269 + -4.25

Combine like terms: -2.41091269 + -4.25 = -6.66091269
v = -6.66091269

Simplifying
v = -6.66091269


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-1.83908731, -6.66091269}
Solution
v = {-1.83908731, -6.66091269}

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