q^2+5q+6.25=0

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Solution for q^2+5q+6.25=0 equation: 


Simplifying
q2 + 5q + 6.25 = 0

Reorder the terms:
6.25 + 5q + q2 = 0

Solving
6.25 + 5q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + 5q + -6.25 + q2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + 5q + q2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + 5q + q2 = 0 + -6.25
5q + q2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
5q + q2 = -6.25

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 = -6.25 + 6.25

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

Combine like terms: -6.25 + 6.25 = 0.00
6.25 + 5q + q2 = 0.00

Factor a perfect square on the left side:
(q + 2.5)(q + 2.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(q + 2.5) equal to 0.00 and 0.00.


Subproblem 1
q + 2.5 = 0.00

Simplifying
q + 2.5 = 0.00

Reorder the terms:
2.5 + q = 0.00

Solving
2.5 + q = 0.00

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 = 0.00 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + q = 0.00 + -2.5
q = 0.00 + -2.5

Combine like terms: 0.00 + -2.5 = -2.5
q = -2.5

Simplifying
q = -2.5


Subproblem 2
q + 2.5 = 0.00

Simplifying
q + 2.5 = 0.00

Reorder the terms:
2.5 + q = 0.00

Solving
2.5 + q = 0.00

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 = 0.00 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + q = 0.00 + -2.5
q = 0.00 + -2.5

Combine like terms: 0.00 + -2.5 = -2.5
q = -2.5

Simplifying
q = -2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-2.5, -2.5}

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