v^2+14v-71=-9

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Solution for v^2+14v-71=-9 equation:


Simplifying
v2 + 14v + -71 = -9

Reorder the terms:
-71 + 14v + v2 = -9

Solving
-71 + 14v + v2 = -9

Solving for variable 'v'.

Reorder the terms:
-71 + 9 + 14v + v2 = -9 + 9

Combine like terms: -71 + 9 = -62
-62 + 14v + v2 = -9 + 9

Combine like terms: -9 + 9 = 0
-62 + 14v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + 14v + 62 + v2 = 0 + 62

Reorder the terms:
-62 + 62 + 14v + v2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + 14v + v2 = 0 + 62
14v + v2 = 0 + 62

Combine like terms: 0 + 62 = 62
14v + v2 = 62

The v term is 14v.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14v + 49 + v2 = 62 + 49

Reorder the terms:
49 + 14v + v2 = 62 + 49

Combine like terms: 62 + 49 = 111
49 + 14v + v2 = 111

Factor a perfect square on the left side:
(v + 7)(v + 7) = 111

Calculate the square root of the right side: 10.535653753

Break this problem into two subproblems by setting 
(v + 7) equal to 10.535653753 and -10.535653753.


Subproblem 1
v + 7 = 10.535653753

Simplifying
v + 7 = 10.535653753

Reorder the terms:
7 + v = 10.535653753

Solving
7 + v = 10.535653753

Solving for variable 'v'.

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

Add '-7' to each side of the equation.
7 + -7 + v = 10.535653753 + -7

Combine like terms: 7 + -7 = 0
0 + v = 10.535653753 + -7
v = 10.535653753 + -7

Combine like terms: 10.535653753 + -7 = 3.535653753
v = 3.535653753

Simplifying
v = 3.535653753


Subproblem 2
v + 7 = -10.535653753

Simplifying
v + 7 = -10.535653753

Reorder the terms:
7 + v = -10.535653753

Solving
7 + v = -10.535653753

Solving for variable 'v'.

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

Add '-7' to each side of the equation.
7 + -7 + v = -10.535653753 + -7

Combine like terms: 7 + -7 = 0
0 + v = -10.535653753 + -7
v = -10.535653753 + -7

Combine like terms: -10.535653753 + -7 = -17.535653753
v = -17.535653753

Simplifying
v = -17.535653753


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {3.535653753, -17.535653753}

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