v^2-14v+49-12=0

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Solution for v^2-14v+49-12=0 equation:


Simplifying
v2 + -14v + 49 + -12 = 0

Reorder the terms:
49 + -12 + -14v + v2 = 0

Combine like terms: 49 + -12 = 37
37 + -14v + v2 = 0

Solving
37 + -14v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + -14v + -37 + v2 = 0 + -37

Reorder the terms:
37 + -37 + -14v + v2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -14v + v2 = 0 + -37
-14v + v2 = 0 + -37

Combine like terms: 0 + -37 = -37
-14v + v2 = -37

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 = -37 + 49

Reorder the terms:
49 + -14v + v2 = -37 + 49

Combine like terms: -37 + 49 = 12
49 + -14v + v2 = 12

Factor a perfect square on the left side:
(v + -7)(v + -7) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(v + -7) equal to 3.464101615 and -3.464101615.

Subproblem 1

v + -7 = 3.464101615 Simplifying v + -7 = 3.464101615 Reorder the terms: -7 + v = 3.464101615 Solving -7 + v = 3.464101615 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 = 3.464101615 + 7 Combine like terms: -7 + 7 = 0 0 + v = 3.464101615 + 7 v = 3.464101615 + 7 Combine like terms: 3.464101615 + 7 = 10.464101615 v = 10.464101615 Simplifying v = 10.464101615

Subproblem 2

v + -7 = -3.464101615 Simplifying v + -7 = -3.464101615 Reorder the terms: -7 + v = -3.464101615 Solving -7 + v = -3.464101615 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 = -3.464101615 + 7 Combine like terms: -7 + 7 = 0 0 + v = -3.464101615 + 7 v = -3.464101615 + 7 Combine like terms: -3.464101615 + 7 = 3.535898385 v = 3.535898385 Simplifying v = 3.535898385

Solution

The solution to the problem is based on the solutions from the subproblems. v = {10.464101615, 3.535898385}

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