48Q-12+12Q+3Q^2=0

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Solution for 48Q-12+12Q+3Q^2=0 equation: 


Simplifying
48Q + -12 + 12Q + 3Q2 = 0

Reorder the terms:
-12 + 48Q + 12Q + 3Q2 = 0

Combine like terms: 48Q + 12Q = 60Q
-12 + 60Q + 3Q2 = 0

Solving
-12 + 60Q + 3Q2 = 0

Solving for variable 'Q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 20Q + Q2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + 20Q + Q2)' equal to zero and attempt to solve:

Simplifying
-4 + 20Q + Q2 = 0

Solving
-4 + 20Q + Q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 20Q + 4 + Q2 = 0 + 4

Reorder the terms:
-4 + 4 + 20Q + Q2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 20Q + Q2 = 0 + 4
20Q + Q2 = 0 + 4

Combine like terms: 0 + 4 = 4
20Q + Q2 = 4

The Q term is 20Q.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20Q + 100 + Q2 = 4 + 100

Reorder the terms:
100 + 20Q + Q2 = 4 + 100

Combine like terms: 4 + 100 = 104
100 + 20Q + Q2 = 104

Factor a perfect square on the left side:
(Q + 10)(Q + 10) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(Q + 10) equal to 10.198039027 and -10.198039027.


Subproblem 1
Q + 10 = 10.198039027

Simplifying
Q + 10 = 10.198039027

Reorder the terms:
10 + Q = 10.198039027

Solving
10 + Q = 10.198039027

Solving for variable 'Q'.

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

Add '-10' to each side of the equation.
10 + -10 + Q = 10.198039027 + -10

Combine like terms: 10 + -10 = 0
0 + Q = 10.198039027 + -10
Q = 10.198039027 + -10

Combine like terms: 10.198039027 + -10 = 0.198039027
Q = 0.198039027

Simplifying
Q = 0.198039027


Subproblem 2
Q + 10 = -10.198039027

Simplifying
Q + 10 = -10.198039027

Reorder the terms:
10 + Q = -10.198039027

Solving
10 + Q = -10.198039027

Solving for variable 'Q'.

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

Add '-10' to each side of the equation.
10 + -10 + Q = -10.198039027 + -10

Combine like terms: 10 + -10 = 0
0 + Q = -10.198039027 + -10
Q = -10.198039027 + -10

Combine like terms: -10.198039027 + -10 = -20.198039027
Q = -20.198039027

Simplifying
Q = -20.198039027


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {0.198039027, -20.198039027}
Solution
Q = {0.198039027, -20.198039027}

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