v^2-14v-47=10

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Solution for v^2-14v-47=10 equation: 


Simplifying
v2 + -14v + -47 = 10

Reorder the terms:
-47 + -14v + v2 = 10

Solving
-47 + -14v + v2 = 10

Solving for variable 'v'.

Reorder the terms:
-47 + -10 + -14v + v2 = 10 + -10

Combine like terms: -47 + -10 = -57
-57 + -14v + v2 = 10 + -10

Combine like terms: 10 + -10 = 0
-57 + -14v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + -14v + 57 + v2 = 0 + 57

Reorder the terms:
-57 + 57 + -14v + v2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + -14v + v2 = 0 + 57
-14v + v2 = 0 + 57

Combine like terms: 0 + 57 = 57
-14v + v2 = 57

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 = 57 + 49

Reorder the terms:
49 + -14v + v2 = 57 + 49

Combine like terms: 57 + 49 = 106
49 + -14v + v2 = 106

Factor a perfect square on the left side:
(v + -7)(v + -7) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(v + -7) equal to 10.295630141 and -10.295630141.


Subproblem 1
v + -7 = 10.295630141

Simplifying
v + -7 = 10.295630141

Reorder the terms:
-7 + v = 10.295630141

Solving
-7 + v = 10.295630141

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 = 10.295630141 + 7

Combine like terms: -7 + 7 = 0
0 + v = 10.295630141 + 7
v = 10.295630141 + 7

Combine like terms: 10.295630141 + 7 = 17.295630141
v = 17.295630141

Simplifying
v = 17.295630141


Subproblem 2
v + -7 = -10.295630141

Simplifying
v + -7 = -10.295630141

Reorder the terms:
-7 + v = -10.295630141

Solving
-7 + v = -10.295630141

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 = -10.295630141 + 7

Combine like terms: -7 + 7 = 0
0 + v = -10.295630141 + 7
v = -10.295630141 + 7

Combine like terms: -10.295630141 + 7 = -3.295630141
v = -3.295630141

Simplifying
v = -3.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {17.295630141, -3.295630141}

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