2v^2+10v+28=v+7+v+7

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Solution for 2v^2+10v+28=v+7+v+7 equation: 


Simplifying
2v2 + 10v + 28 = v + 7 + v + 7

Reorder the terms:
28 + 10v + 2v2 = v + 7 + v + 7

Reorder the terms:
28 + 10v + 2v2 = 7 + 7 + v + v

Combine like terms: 7 + 7 = 14
28 + 10v + 2v2 = 14 + v + v

Combine like terms: v + v = 2v
28 + 10v + 2v2 = 14 + 2v

Solving
28 + 10v + 2v2 = 14 + 2v

Solving for variable 'v'.

Reorder the terms:
28 + -14 + 10v + -2v + 2v2 = 14 + 2v + -14 + -2v

Combine like terms: 28 + -14 = 14
14 + 10v + -2v + 2v2 = 14 + 2v + -14 + -2v

Combine like terms: 10v + -2v = 8v
14 + 8v + 2v2 = 14 + 2v + -14 + -2v

Reorder the terms:
14 + 8v + 2v2 = 14 + -14 + 2v + -2v

Combine like terms: 14 + -14 = 0
14 + 8v + 2v2 = 0 + 2v + -2v
14 + 8v + 2v2 = 2v + -2v

Combine like terms: 2v + -2v = 0
14 + 8v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 4v + v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 4v + v2)' equal to zero and attempt to solve:

Simplifying
7 + 4v + v2 = 0

Solving
7 + 4v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 4v + -7 + v2 = 0 + -7

Reorder the terms:
7 + -7 + 4v + v2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4v + v2 = 0 + -7
4v + v2 = 0 + -7

Combine like terms: 0 + -7 = -7
4v + v2 = -7

The v term is 4v.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4v + 4 + v2 = -7 + 4

Reorder the terms:
4 + 4v + v2 = -7 + 4

Combine like terms: -7 + 4 = -3
4 + 4v + v2 = -3

Factor a perfect square on the left side:
(v + 2)(v + 2) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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