q^2-44q+286=0

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Solution for q^2-44q+286=0 equation: 


Simplifying
q2 + -44q + 286 = 0

Reorder the terms:
286 + -44q + q2 = 0

Solving
286 + -44q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-286' to each side of the equation.
286 + -44q + -286 + q2 = 0 + -286

Reorder the terms:
286 + -286 + -44q + q2 = 0 + -286

Combine like terms: 286 + -286 = 0
0 + -44q + q2 = 0 + -286
-44q + q2 = 0 + -286

Combine like terms: 0 + -286 = -286
-44q + q2 = -286

The q term is -44q.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44q + 484 + q2 = -286 + 484

Reorder the terms:
484 + -44q + q2 = -286 + 484

Combine like terms: -286 + 484 = 198
484 + -44q + q2 = 198

Factor a perfect square on the left side:
(q + -22)(q + -22) = 198

Calculate the square root of the right side: 14.071247279

Break this problem into two subproblems by setting 
(q + -22) equal to 14.071247279 and -14.071247279.


Subproblem 1
q + -22 = 14.071247279

Simplifying
q + -22 = 14.071247279

Reorder the terms:
-22 + q = 14.071247279

Solving
-22 + q = 14.071247279

Solving for variable 'q'.

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

Add '22' to each side of the equation.
-22 + 22 + q = 14.071247279 + 22

Combine like terms: -22 + 22 = 0
0 + q = 14.071247279 + 22
q = 14.071247279 + 22

Combine like terms: 14.071247279 + 22 = 36.071247279
q = 36.071247279

Simplifying
q = 36.071247279


Subproblem 2
q + -22 = -14.071247279

Simplifying
q + -22 = -14.071247279

Reorder the terms:
-22 + q = -14.071247279

Solving
-22 + q = -14.071247279

Solving for variable 'q'.

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

Add '22' to each side of the equation.
-22 + 22 + q = -14.071247279 + 22

Combine like terms: -22 + 22 = 0
0 + q = -14.071247279 + 22
q = -14.071247279 + 22

Combine like terms: -14.071247279 + 22 = 7.928752721
q = 7.928752721

Simplifying
q = 7.928752721


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {36.071247279, 7.928752721}

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