48q^2-600q+24=0

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Solution for 48q^2-600q+24=0 equation: 


Simplifying
48q2 + -600q + 24 = 0

Reorder the terms:
24 + -600q + 48q2 = 0

Solving
24 + -600q + 48q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '24'.
24(1 + -25q + 2q2) = 0

Ignore the factor 24.

Subproblem 1
Set the factor '(1 + -25q + 2q2)' equal to zero and attempt to solve:

Simplifying
1 + -25q + 2q2 = 0

Solving
1 + -25q + 2q2 = 0

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

Divide each side by '2'.
0.5 + -12.5q + q2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -12.5q + -0.5 + q2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -12.5q + q2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -12.5q + q2 = 0 + -0.5
-12.5q + q2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-12.5q + q2 = -0.5

The q term is -12.5q.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5q + 39.0625 + q2 = -0.5 + 39.0625

Reorder the terms:
39.0625 + -12.5q + q2 = -0.5 + 39.0625

Combine like terms: -0.5 + 39.0625 = 38.5625
39.0625 + -12.5q + q2 = 38.5625

Factor a perfect square on the left side:
(q + -6.25)(q + -6.25) = 38.5625

Calculate the square root of the right side: 6.209871174

Break this problem into two subproblems by setting 
(q + -6.25) equal to 6.209871174 and -6.209871174.


Subproblem 1
q + -6.25 = 6.209871174

Simplifying
q + -6.25 = 6.209871174

Reorder the terms:
-6.25 + q = 6.209871174

Solving
-6.25 + q = 6.209871174

Solving for variable 'q'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + q = 6.209871174 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + q = 6.209871174 + 6.25
q = 6.209871174 + 6.25

Combine like terms: 6.209871174 + 6.25 = 12.459871174
q = 12.459871174

Simplifying
q = 12.459871174


Subproblem 2
q + -6.25 = -6.209871174

Simplifying
q + -6.25 = -6.209871174

Reorder the terms:
-6.25 + q = -6.209871174

Solving
-6.25 + q = -6.209871174

Solving for variable 'q'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + q = -6.209871174 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + q = -6.209871174 + 6.25
q = -6.209871174 + 6.25

Combine like terms: -6.209871174 + 6.25 = 0.040128826
q = 0.040128826

Simplifying
q = 0.040128826


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {12.459871174, 0.040128826}
Solution
q = {12.459871174, 0.040128826}

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