v^2-18v-7=0

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Solution for v^2-18v-7=0 equation: 


Simplifying
v2 + -18v + -7 = 0

Reorder the terms:
-7 + -18v + v2 = 0

Solving
-7 + -18v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -18v + 7 + v2 = 0 + 7

Reorder the terms:
-7 + 7 + -18v + v2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -18v + v2 = 0 + 7
-18v + v2 = 0 + 7

Combine like terms: 0 + 7 = 7
-18v + v2 = 7

The v term is -18v.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18v + 81 + v2 = 7 + 81

Reorder the terms:
81 + -18v + v2 = 7 + 81

Combine like terms: 7 + 81 = 88
81 + -18v + v2 = 88

Factor a perfect square on the left side:
(v + -9)(v + -9) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(v + -9) equal to 9.38083152 and -9.38083152.


Subproblem 1
v + -9 = 9.38083152

Simplifying
v + -9 = 9.38083152

Reorder the terms:
-9 + v = 9.38083152

Solving
-9 + v = 9.38083152

Solving for variable 'v'.

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

Add '9' to each side of the equation.
-9 + 9 + v = 9.38083152 + 9

Combine like terms: -9 + 9 = 0
0 + v = 9.38083152 + 9
v = 9.38083152 + 9

Combine like terms: 9.38083152 + 9 = 18.38083152
v = 18.38083152

Simplifying
v = 18.38083152


Subproblem 2
v + -9 = -9.38083152

Simplifying
v + -9 = -9.38083152

Reorder the terms:
-9 + v = -9.38083152

Solving
-9 + v = -9.38083152

Solving for variable 'v'.

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

Add '9' to each side of the equation.
-9 + 9 + v = -9.38083152 + 9

Combine like terms: -9 + 9 = 0
0 + v = -9.38083152 + 9
v = -9.38083152 + 9

Combine like terms: -9.38083152 + 9 = -0.38083152
v = -0.38083152

Simplifying
v = -0.38083152


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {18.38083152, -0.38083152}

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