48+4q+3q^2=100

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Solution for 48+4q+3q^2=100 equation: 


Simplifying
48 + 4q + 3q2 = 100

Solving
48 + 4q + 3q2 = 100

Solving for variable 'q'.

Reorder the terms:
48 + -100 + 4q + 3q2 = 100 + -100

Combine like terms: 48 + -100 = -52
-52 + 4q + 3q2 = 100 + -100

Combine like terms: 100 + -100 = 0
-52 + 4q + 3q2 = 0

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

Divide each side by '3'.
-17.33333333 + 1.333333333q + q2 = 0

Move the constant term to the right:

Add '17.33333333' to each side of the equation.
-17.33333333 + 1.333333333q + 17.33333333 + q2 = 0 + 17.33333333

Reorder the terms:
-17.33333333 + 17.33333333 + 1.333333333q + q2 = 0 + 17.33333333

Combine like terms: -17.33333333 + 17.33333333 = 0.00000000
0.00000000 + 1.333333333q + q2 = 0 + 17.33333333
1.333333333q + q2 = 0 + 17.33333333

Combine like terms: 0 + 17.33333333 = 17.33333333
1.333333333q + q2 = 17.33333333

The q term is 1.333333333q.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333q + 0.4444444442 + q2 = 17.33333333 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333q + q2 = 17.33333333 + 0.4444444442

Combine like terms: 17.33333333 + 0.4444444442 = 17.7777777742
0.4444444442 + 1.333333333q + q2 = 17.7777777742

Factor a perfect square on the left side:
(q + 0.6666666665)(q + 0.6666666665) = 17.7777777742

Calculate the square root of the right side: 4.216370213

Break this problem into two subproblems by setting 
(q + 0.6666666665) equal to 4.216370213 and -4.216370213.


Subproblem 1
q + 0.6666666665 = 4.216370213

Simplifying
q + 0.6666666665 = 4.216370213

Reorder the terms:
0.6666666665 + q = 4.216370213

Solving
0.6666666665 + q = 4.216370213

Solving for variable 'q'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + q = 4.216370213 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + q = 4.216370213 + -0.6666666665
q = 4.216370213 + -0.6666666665

Combine like terms: 4.216370213 + -0.6666666665 = 3.5497035465
q = 3.5497035465

Simplifying
q = 3.5497035465


Subproblem 2
q + 0.6666666665 = -4.216370213

Simplifying
q + 0.6666666665 = -4.216370213

Reorder the terms:
0.6666666665 + q = -4.216370213

Solving
0.6666666665 + q = -4.216370213

Solving for variable 'q'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + q = -4.216370213 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + q = -4.216370213 + -0.6666666665
q = -4.216370213 + -0.6666666665

Combine like terms: -4.216370213 + -0.6666666665 = -4.8830368795
q = -4.8830368795

Simplifying
q = -4.8830368795


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {3.5497035465, -4.8830368795}

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