0=5q^2+25q-100

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Solution for 0=5q^2+25q-100 equation: 


Simplifying
0 = 5q2 + 25q + -100

Reorder the terms:
0 = -100 + 25q + 5q2

Solving
0 = -100 + 25q + 5q2

Solving for variable 'q'.

Combine like terms: 0 + 100 = 100
100 + -25q + -5q2 = -100 + 25q + 5q2 + 100 + -25q + -5q2

Reorder the terms:
100 + -25q + -5q2 = -100 + 100 + 25q + -25q + 5q2 + -5q2

Combine like terms: -100 + 100 = 0
100 + -25q + -5q2 = 0 + 25q + -25q + 5q2 + -5q2
100 + -25q + -5q2 = 25q + -25q + 5q2 + -5q2

Combine like terms: 25q + -25q = 0
100 + -25q + -5q2 = 0 + 5q2 + -5q2
100 + -25q + -5q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
100 + -25q + -5q2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + -5q + -1q2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(20 + -5q + -1q2)' equal to zero and attempt to solve:

Simplifying
20 + -5q + -1q2 = 0

Solving
20 + -5q + -1q2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-20 + 5q + q2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 5q + 20 + q2 = 0 + 20

Reorder the terms:
-20 + 20 + 5q + q2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 5q + q2 = 0 + 20
5q + q2 = 0 + 20

Combine like terms: 0 + 20 = 20
5q + q2 = 20

The q term is 5q.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5q + 6.25 + q2 = 20 + 6.25

Reorder the terms:
6.25 + 5q + q2 = 20 + 6.25

Combine like terms: 20 + 6.25 = 26.25
6.25 + 5q + q2 = 26.25

Factor a perfect square on the left side:
(q + 2.5)(q + 2.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(q + 2.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
q + 2.5 = 5.123475383

Simplifying
q + 2.5 = 5.123475383

Reorder the terms:
2.5 + q = 5.123475383

Solving
2.5 + q = 5.123475383

Solving for variable 'q'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + q = 5.123475383 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + q = 5.123475383 + -2.5
q = 5.123475383 + -2.5

Combine like terms: 5.123475383 + -2.5 = 2.623475383
q = 2.623475383

Simplifying
q = 2.623475383


Subproblem 2
q + 2.5 = -5.123475383

Simplifying
q + 2.5 = -5.123475383

Reorder the terms:
2.5 + q = -5.123475383

Solving
2.5 + q = -5.123475383

Solving for variable 'q'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + q = -5.123475383 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + q = -5.123475383 + -2.5
q = -5.123475383 + -2.5

Combine like terms: -5.123475383 + -2.5 = -7.623475383
q = -7.623475383

Simplifying
q = -7.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {2.623475383, -7.623475383}
Solution
q = {2.623475383, -7.623475383}

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