v^2+22v=37

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Solution for v^2+22v=37 equation:


Simplifying
v2 + 22v = 37

Reorder the terms:
22v + v2 = 37

Solving
22v + v2 = 37

Solving for variable 'v'.

Reorder the terms:
-37 + 22v + v2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + 22v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 22v + 37 + v2 = 0 + 37

Reorder the terms:
-37 + 37 + 22v + v2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 22v + v2 = 0 + 37
22v + v2 = 0 + 37

Combine like terms: 0 + 37 = 37
22v + v2 = 37

The v term is 22v.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22v + 121 + v2 = 37 + 121

Reorder the terms:
121 + 22v + v2 = 37 + 121

Combine like terms: 37 + 121 = 158
121 + 22v + v2 = 158

Factor a perfect square on the left side:
(v + 11)(v + 11) = 158

Calculate the square root of the right side: 12.56980509

Break this problem into two subproblems by setting 
(v + 11) equal to 12.56980509 and -12.56980509.

Subproblem 1

v + 11 = 12.56980509 Simplifying v + 11 = 12.56980509 Reorder the terms: 11 + v = 12.56980509 Solving 11 + v = 12.56980509 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + v = 12.56980509 + -11 Combine like terms: 11 + -11 = 0 0 + v = 12.56980509 + -11 v = 12.56980509 + -11 Combine like terms: 12.56980509 + -11 = 1.56980509 v = 1.56980509 Simplifying v = 1.56980509

Subproblem 2

v + 11 = -12.56980509 Simplifying v + 11 = -12.56980509 Reorder the terms: 11 + v = -12.56980509 Solving 11 + v = -12.56980509 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + v = -12.56980509 + -11 Combine like terms: 11 + -11 = 0 0 + v = -12.56980509 + -11 v = -12.56980509 + -11 Combine like terms: -12.56980509 + -11 = -23.56980509 v = -23.56980509 Simplifying v = -23.56980509

Solution

The solution to the problem is based on the solutions from the subproblems. v = {1.56980509, -23.56980509}

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