v^2+16v=65

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Solution for v^2+16v=65 equation:


Simplifying
v2 + 16v = 65

Reorder the terms:
16v + v2 = 65

Solving
16v + v2 = 65

Solving for variable 'v'.

Reorder the terms:
-65 + 16v + v2 = 65 + -65

Combine like terms: 65 + -65 = 0
-65 + 16v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + 16v + 65 + v2 = 0 + 65

Reorder the terms:
-65 + 65 + 16v + v2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + 16v + v2 = 0 + 65
16v + v2 = 0 + 65

Combine like terms: 0 + 65 = 65
16v + v2 = 65

The v term is 16v.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16v + 64 + v2 = 65 + 64

Reorder the terms:
64 + 16v + v2 = 65 + 64

Combine like terms: 65 + 64 = 129
64 + 16v + v2 = 129

Factor a perfect square on the left side:
(v + 8)(v + 8) = 129

Calculate the square root of the right side: 11.357816692

Break this problem into two subproblems by setting 
(v + 8) equal to 11.357816692 and -11.357816692.

Subproblem 1

v + 8 = 11.357816692 Simplifying v + 8 = 11.357816692 Reorder the terms: 8 + v = 11.357816692 Solving 8 + v = 11.357816692 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + v = 11.357816692 + -8 Combine like terms: 8 + -8 = 0 0 + v = 11.357816692 + -8 v = 11.357816692 + -8 Combine like terms: 11.357816692 + -8 = 3.357816692 v = 3.357816692 Simplifying v = 3.357816692

Subproblem 2

v + 8 = -11.357816692 Simplifying v + 8 = -11.357816692 Reorder the terms: 8 + v = -11.357816692 Solving 8 + v = -11.357816692 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + v = -11.357816692 + -8 Combine like terms: 8 + -8 = 0 0 + v = -11.357816692 + -8 v = -11.357816692 + -8 Combine like terms: -11.357816692 + -8 = -19.357816692 v = -19.357816692 Simplifying v = -19.357816692

Solution

The solution to the problem is based on the solutions from the subproblems. v = {3.357816692, -19.357816692}

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