q^2-2.67q-60=0

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Solution for q^2-2.67q-60=0 equation: 


Simplifying
q2 + -2.67q + -60 = 0

Reorder the terms:
-60 + -2.67q + q2 = 0

Solving
-60 + -2.67q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -2.67q + 60 + q2 = 0 + 60

Reorder the terms:
-60 + 60 + -2.67q + q2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -2.67q + q2 = 0 + 60
-2.67q + q2 = 0 + 60

Combine like terms: 0 + 60 = 60
-2.67q + q2 = 60

The q term is -2.67q.  Take half its coefficient (-1.335).
Square it (1.782225) and add it to both sides.

Add '1.782225' to each side of the equation.
-2.67q + 1.782225 + q2 = 60 + 1.782225

Reorder the terms:
1.782225 + -2.67q + q2 = 60 + 1.782225

Combine like terms: 60 + 1.782225 = 61.782225
1.782225 + -2.67q + q2 = 61.782225

Factor a perfect square on the left side:
(q + -1.335)(q + -1.335) = 61.782225

Calculate the square root of the right side: 7.860166983

Break this problem into two subproblems by setting 
(q + -1.335) equal to 7.860166983 and -7.860166983.


Subproblem 1
q + -1.335 = 7.860166983

Simplifying
q + -1.335 = 7.860166983

Reorder the terms:
-1.335 + q = 7.860166983

Solving
-1.335 + q = 7.860166983

Solving for variable 'q'.

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

Add '1.335' to each side of the equation.
-1.335 + 1.335 + q = 7.860166983 + 1.335

Combine like terms: -1.335 + 1.335 = 0.000
0.000 + q = 7.860166983 + 1.335
q = 7.860166983 + 1.335

Combine like terms: 7.860166983 + 1.335 = 9.195166983
q = 9.195166983

Simplifying
q = 9.195166983


Subproblem 2
q + -1.335 = -7.860166983

Simplifying
q + -1.335 = -7.860166983

Reorder the terms:
-1.335 + q = -7.860166983

Solving
-1.335 + q = -7.860166983

Solving for variable 'q'.

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

Add '1.335' to each side of the equation.
-1.335 + 1.335 + q = -7.860166983 + 1.335

Combine like terms: -1.335 + 1.335 = 0.000
0.000 + q = -7.860166983 + 1.335
q = -7.860166983 + 1.335

Combine like terms: -7.860166983 + 1.335 = -6.525166983
q = -6.525166983

Simplifying
q = -6.525166983


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {9.195166983, -6.525166983}

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