q^2-15q+8=0

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Solution for q^2-15q+8=0 equation: 


Simplifying
q2 + -15q + 8 = 0

Reorder the terms:
8 + -15q + q2 = 0

Solving
8 + -15q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -15q + -8 + q2 = 0 + -8

Reorder the terms:
8 + -8 + -15q + q2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -15q + q2 = 0 + -8
-15q + q2 = 0 + -8

Combine like terms: 0 + -8 = -8
-15q + q2 = -8

The q term is -15q.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15q + 56.25 + q2 = -8 + 56.25

Reorder the terms:
56.25 + -15q + q2 = -8 + 56.25

Combine like terms: -8 + 56.25 = 48.25
56.25 + -15q + q2 = 48.25

Factor a perfect square on the left side:
(q + -7.5)(q + -7.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(q + -7.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
q + -7.5 = 6.946221995

Simplifying
q + -7.5 = 6.946221995

Reorder the terms:
-7.5 + q = 6.946221995

Solving
-7.5 + q = 6.946221995

Solving for variable 'q'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + q = 6.946221995 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + q = 6.946221995 + 7.5
q = 6.946221995 + 7.5

Combine like terms: 6.946221995 + 7.5 = 14.446221995
q = 14.446221995

Simplifying
q = 14.446221995


Subproblem 2
q + -7.5 = -6.946221995

Simplifying
q + -7.5 = -6.946221995

Reorder the terms:
-7.5 + q = -6.946221995

Solving
-7.5 + q = -6.946221995

Solving for variable 'q'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + q = -6.946221995 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + q = -6.946221995 + 7.5
q = -6.946221995 + 7.5

Combine like terms: -6.946221995 + 7.5 = 0.553778005
q = 0.553778005

Simplifying
q = 0.553778005


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {14.446221995, 0.553778005}

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