2v^2-24v-42=0

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Solution for 2v^2-24v-42=0 equation: 


Simplifying
2v2 + -24v + -42 = 0

Reorder the terms:
-42 + -24v + 2v2 = 0

Solving
-42 + -24v + 2v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -12v + v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + -12v + v2)' equal to zero and attempt to solve:

Simplifying
-21 + -12v + v2 = 0

Solving
-21 + -12v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -12v + 21 + v2 = 0 + 21

Reorder the terms:
-21 + 21 + -12v + v2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -12v + v2 = 0 + 21
-12v + v2 = 0 + 21

Combine like terms: 0 + 21 = 21
-12v + v2 = 21

The v term is -12v.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12v + 36 + v2 = 21 + 36

Reorder the terms:
36 + -12v + v2 = 21 + 36

Combine like terms: 21 + 36 = 57
36 + -12v + v2 = 57

Factor a perfect square on the left side:
(v + -6)(v + -6) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(v + -6) equal to 7.549834435 and -7.549834435.


Subproblem 1
v + -6 = 7.549834435

Simplifying
v + -6 = 7.549834435

Reorder the terms:
-6 + v = 7.549834435

Solving
-6 + v = 7.549834435

Solving for variable 'v'.

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

Add '6' to each side of the equation.
-6 + 6 + v = 7.549834435 + 6

Combine like terms: -6 + 6 = 0
0 + v = 7.549834435 + 6
v = 7.549834435 + 6

Combine like terms: 7.549834435 + 6 = 13.549834435
v = 13.549834435

Simplifying
v = 13.549834435


Subproblem 2
v + -6 = -7.549834435

Simplifying
v + -6 = -7.549834435

Reorder the terms:
-6 + v = -7.549834435

Solving
-6 + v = -7.549834435

Solving for variable 'v'.

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

Add '6' to each side of the equation.
-6 + 6 + v = -7.549834435 + 6

Combine like terms: -6 + 6 = 0
0 + v = -7.549834435 + 6
v = -7.549834435 + 6

Combine like terms: -7.549834435 + 6 = -1.549834435
v = -1.549834435

Simplifying
v = -1.549834435


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {13.549834435, -1.549834435}
Solution
v = {13.549834435, -1.549834435}

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