v^2-12v=37

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Solution for v^2-12v=37 equation:


Simplifying
v2 + -12v = 37

Reorder the terms:
-12v + v2 = 37

Solving
-12v + v2 = 37

Solving for variable 'v'.

Reorder the terms:
-37 + -12v + v2 = 37 + -37

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

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -12v + 37 + v2 = 0 + 37

Reorder the terms:
-37 + 37 + -12v + v2 = 0 + 37

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

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

The v term is -12v.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12v + 36 + v2 = 37 + 36

Reorder the terms:
36 + -12v + v2 = 37 + 36

Combine like terms: 37 + 36 = 73
36 + -12v + v2 = 73

Factor a perfect square on the left side:
(v + -6)(v + -6) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(v + -6) equal to 8.544003745 and -8.544003745.

Subproblem 1

v + -6 = 8.544003745 Simplifying v + -6 = 8.544003745 Reorder the terms: -6 + v = 8.544003745 Solving -6 + v = 8.544003745 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = 8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + v = 8.544003745 + 6 v = 8.544003745 + 6 Combine like terms: 8.544003745 + 6 = 14.544003745 v = 14.544003745 Simplifying v = 14.544003745

Subproblem 2

v + -6 = -8.544003745 Simplifying v + -6 = -8.544003745 Reorder the terms: -6 + v = -8.544003745 Solving -6 + v = -8.544003745 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = -8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + v = -8.544003745 + 6 v = -8.544003745 + 6 Combine like terms: -8.544003745 + 6 = -2.544003745 v = -2.544003745 Simplifying v = -2.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. v = {14.544003745, -2.544003745}

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