v^2-18v-68=0

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Solution for v^2-18v-68=0 equation: 


Simplifying
v2 + -18v + -68 = 0

Reorder the terms:
-68 + -18v + v2 = 0

Solving
-68 + -18v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + -18v + 68 + v2 = 0 + 68

Reorder the terms:
-68 + 68 + -18v + v2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + -18v + v2 = 0 + 68
-18v + v2 = 0 + 68

Combine like terms: 0 + 68 = 68
-18v + v2 = 68

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 = 68 + 81

Reorder the terms:
81 + -18v + v2 = 68 + 81

Combine like terms: 68 + 81 = 149
81 + -18v + v2 = 149

Factor a perfect square on the left side:
(v + -9)(v + -9) = 149

Calculate the square root of the right side: 12.206555616

Break this problem into two subproblems by setting 
(v + -9) equal to 12.206555616 and -12.206555616.


Subproblem 1
v + -9 = 12.206555616

Simplifying
v + -9 = 12.206555616

Reorder the terms:
-9 + v = 12.206555616

Solving
-9 + v = 12.206555616

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 = 12.206555616 + 9

Combine like terms: -9 + 9 = 0
0 + v = 12.206555616 + 9
v = 12.206555616 + 9

Combine like terms: 12.206555616 + 9 = 21.206555616
v = 21.206555616

Simplifying
v = 21.206555616


Subproblem 2
v + -9 = -12.206555616

Simplifying
v + -9 = -12.206555616

Reorder the terms:
-9 + v = -12.206555616

Solving
-9 + v = -12.206555616

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 = -12.206555616 + 9

Combine like terms: -9 + 9 = 0
0 + v = -12.206555616 + 9
v = -12.206555616 + 9

Combine like terms: -12.206555616 + 9 = -3.206555616
v = -3.206555616

Simplifying
v = -3.206555616


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {21.206555616, -3.206555616}

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