8v^2-30v-18=0

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Solution for 8v^2-30v-18=0 equation: 


Simplifying
8v2 + -30v + -18 = 0

Reorder the terms:
-18 + -30v + 8v2 = 0

Solving
-18 + -30v + 8v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -15v + 4v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -15v + 4v2)' equal to zero and attempt to solve:

Simplifying
-9 + -15v + 4v2 = 0

Solving
-9 + -15v + 4v2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-2.25 + -3.75v + v2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -3.75v + 2.25 + v2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -3.75v + v2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -3.75v + v2 = 0 + 2.25
-3.75v + v2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-3.75v + v2 = 2.25

The v term is -3.75v.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75v + 3.515625 + v2 = 2.25 + 3.515625

Reorder the terms:
3.515625 + -3.75v + v2 = 2.25 + 3.515625

Combine like terms: 2.25 + 3.515625 = 5.765625
3.515625 + -3.75v + v2 = 5.765625

Factor a perfect square on the left side:
(v + -1.875)(v + -1.875) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(v + -1.875) equal to 2.401171589 and -2.401171589.


Subproblem 1
v + -1.875 = 2.401171589

Simplifying
v + -1.875 = 2.401171589

Reorder the terms:
-1.875 + v = 2.401171589

Solving
-1.875 + v = 2.401171589

Solving for variable 'v'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + v = 2.401171589 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + v = 2.401171589 + 1.875
v = 2.401171589 + 1.875

Combine like terms: 2.401171589 + 1.875 = 4.276171589
v = 4.276171589

Simplifying
v = 4.276171589


Subproblem 2
v + -1.875 = -2.401171589

Simplifying
v + -1.875 = -2.401171589

Reorder the terms:
-1.875 + v = -2.401171589

Solving
-1.875 + v = -2.401171589

Solving for variable 'v'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + v = -2.401171589 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + v = -2.401171589 + 1.875
v = -2.401171589 + 1.875

Combine like terms: -2.401171589 + 1.875 = -0.526171589
v = -0.526171589

Simplifying
v = -0.526171589


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {4.276171589, -0.526171589}
Solution
v = {4.276171589, -0.526171589}

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