-4v^2+33v-48=0

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Solution for -4v^2+33v-48=0 equation:


Simplifying
-4v2 + 33v + -48 = 0

Reorder the terms:
-48 + 33v + -4v2 = 0

Solving
-48 + 33v + -4v2 = 0

Solving for variable 'v'.

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

Divide each side by '-4'.
12 + -8.25v + v2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -8.25v + -12 + v2 = 0 + -12

Reorder the terms:
12 + -12 + -8.25v + v2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -8.25v + v2 = 0 + -12
-8.25v + v2 = 0 + -12

Combine like terms: 0 + -12 = -12
-8.25v + v2 = -12

The v term is -8.25v.  Take half its coefficient (-4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
-8.25v + 17.015625 + v2 = -12 + 17.015625

Reorder the terms:
17.015625 + -8.25v + v2 = -12 + 17.015625

Combine like terms: -12 + 17.015625 = 5.015625
17.015625 + -8.25v + v2 = 5.015625

Factor a perfect square on the left side:
(v + -4.125)(v + -4.125) = 5.015625

Calculate the square root of the right side: 2.239559108

Break this problem into two subproblems by setting 
(v + -4.125) equal to 2.239559108 and -2.239559108.


Subproblem 1
v + -4.125 = 2.239559108

Simplifying
v + -4.125 = 2.239559108

Reorder the terms:
-4.125 + v = 2.239559108

Solving
-4.125 + v = 2.239559108

Solving for variable 'v'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + v = 2.239559108 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + v = 2.239559108 + 4.125
v = 2.239559108 + 4.125

Combine like terms: 2.239559108 + 4.125 = 6.364559108
v = 6.364559108

Simplifying
v = 6.364559108


Subproblem 2
v + -4.125 = -2.239559108

Simplifying
v + -4.125 = -2.239559108

Reorder the terms:
-4.125 + v = -2.239559108

Solving
-4.125 + v = -2.239559108

Solving for variable 'v'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + v = -2.239559108 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + v = -2.239559108 + 4.125
v = -2.239559108 + 4.125

Combine like terms: -2.239559108 + 4.125 = 1.885440892
v = 1.885440892

Simplifying
v = 1.885440892


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {6.364559108, 1.885440892}

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