v^2+8v-52=0

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Solution for v^2+8v-52=0 equation: 


Simplifying
v2 + 8v + -52 = 0

Reorder the terms:
-52 + 8v + v2 = 0

Solving
-52 + 8v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 8v + 52 + v2 = 0 + 52

Reorder the terms:
-52 + 52 + 8v + v2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 8v + v2 = 0 + 52
8v + v2 = 0 + 52

Combine like terms: 0 + 52 = 52
8v + v2 = 52

The v term is 8v.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8v + 16 + v2 = 52 + 16

Reorder the terms:
16 + 8v + v2 = 52 + 16

Combine like terms: 52 + 16 = 68
16 + 8v + v2 = 68

Factor a perfect square on the left side:
(v + 4)(v + 4) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(v + 4) equal to 8.246211251 and -8.246211251.


Subproblem 1
v + 4 = 8.246211251

Simplifying
v + 4 = 8.246211251

Reorder the terms:
4 + v = 8.246211251

Solving
4 + v = 8.246211251

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + v = 8.246211251 + -4

Combine like terms: 4 + -4 = 0
0 + v = 8.246211251 + -4
v = 8.246211251 + -4

Combine like terms: 8.246211251 + -4 = 4.246211251
v = 4.246211251

Simplifying
v = 4.246211251


Subproblem 2
v + 4 = -8.246211251

Simplifying
v + 4 = -8.246211251

Reorder the terms:
4 + v = -8.246211251

Solving
4 + v = -8.246211251

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + v = -8.246211251 + -4

Combine like terms: 4 + -4 = 0
0 + v = -8.246211251 + -4
v = -8.246211251 + -4

Combine like terms: -8.246211251 + -4 = -12.246211251
v = -12.246211251

Simplifying
v = -12.246211251


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {4.246211251, -12.246211251}

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