-3v^2-5v+24=0

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Solution for -3v^2-5v+24=0 equation: 


Simplifying
-3v2 + -5v + 24 = 0

Reorder the terms:
24 + -5v + -3v2 = 0

Solving
24 + -5v + -3v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-8 + 1.666666667v + v2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 1.666666667v + 8 + v2 = 0 + 8

Reorder the terms:
-8 + 8 + 1.666666667v + v2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 1.666666667v + v2 = 0 + 8
1.666666667v + v2 = 0 + 8

Combine like terms: 0 + 8 = 8
1.666666667v + v2 = 8

The v term is 1.666666667v.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667v + 0.6944444447 + v2 = 8 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667v + v2 = 8 + 0.6944444447

Combine like terms: 8 + 0.6944444447 = 8.6944444447
0.6944444447 + 1.666666667v + v2 = 8.6944444447

Factor a perfect square on the left side:
(v + 0.8333333335)(v + 0.8333333335) = 8.6944444447

Calculate the square root of the right side: 2.948634336

Break this problem into two subproblems by setting 
(v + 0.8333333335) equal to 2.948634336 and -2.948634336.


Subproblem 1
v + 0.8333333335 = 2.948634336

Simplifying
v + 0.8333333335 = 2.948634336

Reorder the terms:
0.8333333335 + v = 2.948634336

Solving
0.8333333335 + v = 2.948634336

Solving for variable 'v'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + v = 2.948634336 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + v = 2.948634336 + -0.8333333335
v = 2.948634336 + -0.8333333335

Combine like terms: 2.948634336 + -0.8333333335 = 2.1153010025
v = 2.1153010025

Simplifying
v = 2.1153010025


Subproblem 2
v + 0.8333333335 = -2.948634336

Simplifying
v + 0.8333333335 = -2.948634336

Reorder the terms:
0.8333333335 + v = -2.948634336

Solving
0.8333333335 + v = -2.948634336

Solving for variable 'v'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + v = -2.948634336 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + v = -2.948634336 + -0.8333333335
v = -2.948634336 + -0.8333333335

Combine like terms: -2.948634336 + -0.8333333335 = -3.7819676695
v = -3.7819676695

Simplifying
v = -3.7819676695


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.1153010025, -3.7819676695}

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