2v^2-14v+25=v^2+4

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Solution for 2v^2-14v+25=v^2+4 equation:


Simplifying
2v2 + -14v + 25 = v2 + 4

Reorder the terms:
25 + -14v + 2v2 = v2 + 4

Reorder the terms:
25 + -14v + 2v2 = 4 + v2

Solving
25 + -14v + 2v2 = 4 + v2

Solving for variable 'v'.

Reorder the terms:
25 + -4 + -14v + 2v2 + -1v2 = 4 + v2 + -4 + -1v2

Combine like terms: 25 + -4 = 21
21 + -14v + 2v2 + -1v2 = 4 + v2 + -4 + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
21 + -14v + 1v2 = 4 + v2 + -4 + -1v2

Reorder the terms:
21 + -14v + 1v2 = 4 + -4 + v2 + -1v2

Combine like terms: 4 + -4 = 0
21 + -14v + 1v2 = 0 + v2 + -1v2
21 + -14v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
21 + -14v + 1v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -14v + -21 + v2 = 0 + -21

Reorder the terms:
21 + -21 + -14v + v2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -14v + v2 = 0 + -21
-14v + v2 = 0 + -21

Combine like terms: 0 + -21 = -21
-14v + v2 = -21

The v term is -14v.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14v + 49 + v2 = -21 + 49

Reorder the terms:
49 + -14v + v2 = -21 + 49

Combine like terms: -21 + 49 = 28
49 + -14v + v2 = 28

Factor a perfect square on the left side:
(v + -7)(v + -7) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(v + -7) equal to 5.291502622 and -5.291502622.

Subproblem 1

v + -7 = 5.291502622 Simplifying v + -7 = 5.291502622 Reorder the terms: -7 + v = 5.291502622 Solving -7 + v = 5.291502622 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = 5.291502622 + 7 Combine like terms: -7 + 7 = 0 0 + v = 5.291502622 + 7 v = 5.291502622 + 7 Combine like terms: 5.291502622 + 7 = 12.291502622 v = 12.291502622 Simplifying v = 12.291502622

Subproblem 2

v + -7 = -5.291502622 Simplifying v + -7 = -5.291502622 Reorder the terms: -7 + v = -5.291502622 Solving -7 + v = -5.291502622 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = -5.291502622 + 7 Combine like terms: -7 + 7 = 0 0 + v = -5.291502622 + 7 v = -5.291502622 + 7 Combine like terms: -5.291502622 + 7 = 1.708497378 v = 1.708497378 Simplifying v = 1.708497378

Solution

The solution to the problem is based on the solutions from the subproblems. v = {12.291502622, 1.708497378}

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