-.03q^2-1.4q-4=0

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Solution for -.03q^2-1.4q-4=0 equation: 


Simplifying
-0.03q2 + -1.4q + -4 = 0

Reorder the terms:
-4 + -1.4q + -0.03q2 = 0

Solving
-4 + -1.4q + -0.03q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
-0.03 the coefficient of the squared term: 

Divide each side by '-0.03'.
133.3333333 + 46.66666667q + q2 = 0

Move the constant term to the right:

Add '-133.3333333' to each side of the equation.
133.3333333 + 46.66666667q + -133.3333333 + q2 = 0 + -133.3333333

Reorder the terms:
133.3333333 + -133.3333333 + 46.66666667q + q2 = 0 + -133.3333333

Combine like terms: 133.3333333 + -133.3333333 = 0.0000000
0.0000000 + 46.66666667q + q2 = 0 + -133.3333333
46.66666667q + q2 = 0 + -133.3333333

Combine like terms: 0 + -133.3333333 = -133.3333333
46.66666667q + q2 = -133.3333333

The q term is 46.66666667q.  Take half its coefficient (23.33333334).
Square it (544.4444448) and add it to both sides.

Add '544.4444448' to each side of the equation.
46.66666667q + 544.4444448 + q2 = -133.3333333 + 544.4444448

Reorder the terms:
544.4444448 + 46.66666667q + q2 = -133.3333333 + 544.4444448

Combine like terms: -133.3333333 + 544.4444448 = 411.1111115
544.4444448 + 46.66666667q + q2 = 411.1111115

Factor a perfect square on the left side:
(q + 23.33333334)(q + 23.33333334) = 411.1111115

Calculate the square root of the right side: 20.275875111

Break this problem into two subproblems by setting 
(q + 23.33333334) equal to 20.275875111 and -20.275875111.


Subproblem 1
q + 23.33333334 = 20.275875111

Simplifying
q + 23.33333334 = 20.275875111

Reorder the terms:
23.33333334 + q = 20.275875111

Solving
23.33333334 + q = 20.275875111

Solving for variable 'q'.

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

Add '-23.33333334' to each side of the equation.
23.33333334 + -23.33333334 + q = 20.275875111 + -23.33333334

Combine like terms: 23.33333334 + -23.33333334 = 0.00000000
0.00000000 + q = 20.275875111 + -23.33333334
q = 20.275875111 + -23.33333334

Combine like terms: 20.275875111 + -23.33333334 = -3.057458229
q = -3.057458229

Simplifying
q = -3.057458229


Subproblem 2
q + 23.33333334 = -20.275875111

Simplifying
q + 23.33333334 = -20.275875111

Reorder the terms:
23.33333334 + q = -20.275875111

Solving
23.33333334 + q = -20.275875111

Solving for variable 'q'.

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

Add '-23.33333334' to each side of the equation.
23.33333334 + -23.33333334 + q = -20.275875111 + -23.33333334

Combine like terms: 23.33333334 + -23.33333334 = 0.00000000
0.00000000 + q = -20.275875111 + -23.33333334
q = -20.275875111 + -23.33333334

Combine like terms: -20.275875111 + -23.33333334 = -43.609208451
q = -43.609208451

Simplifying
q = -43.609208451


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-3.057458229, -43.609208451}

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