v^2+16v=-27

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Solution for v^2+16v=-27 equation:


Simplifying
v2 + 16v = -27

Reorder the terms:
16v + v2 = -27

Solving
16v + v2 = -27

Solving for variable 'v'.

Reorder the terms:
27 + 16v + v2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 16v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 16v + -27 + v2 = 0 + -27

Reorder the terms:
27 + -27 + 16v + v2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 16v + v2 = 0 + -27
16v + v2 = 0 + -27

Combine like terms: 0 + -27 = -27
16v + v2 = -27

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 = -27 + 64

Reorder the terms:
64 + 16v + v2 = -27 + 64

Combine like terms: -27 + 64 = 37
64 + 16v + v2 = 37

Factor a perfect square on the left side:
(v + 8)(v + 8) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(v + 8) equal to 6.08276253 and -6.08276253.

Subproblem 1

v + 8 = 6.08276253 Simplifying v + 8 = 6.08276253 Reorder the terms: 8 + v = 6.08276253 Solving 8 + v = 6.08276253 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 = 6.08276253 + -8 Combine like terms: 8 + -8 = 0 0 + v = 6.08276253 + -8 v = 6.08276253 + -8 Combine like terms: 6.08276253 + -8 = -1.91723747 v = -1.91723747 Simplifying v = -1.91723747

Subproblem 2

v + 8 = -6.08276253 Simplifying v + 8 = -6.08276253 Reorder the terms: 8 + v = -6.08276253 Solving 8 + v = -6.08276253 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 = -6.08276253 + -8 Combine like terms: 8 + -8 = 0 0 + v = -6.08276253 + -8 v = -6.08276253 + -8 Combine like terms: -6.08276253 + -8 = -14.08276253 v = -14.08276253 Simplifying v = -14.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. v = {-1.91723747, -14.08276253}

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