2q^2+22q-1054=0

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Solution for 2q^2+22q-1054=0 equation: 


Simplifying
2q2 + 22q + -1054 = 0

Reorder the terms:
-1054 + 22q + 2q2 = 0

Solving
-1054 + 22q + 2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-527 + 11q + q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-527 + 11q + q2)' equal to zero and attempt to solve:

Simplifying
-527 + 11q + q2 = 0

Solving
-527 + 11q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '527' to each side of the equation.
-527 + 11q + 527 + q2 = 0 + 527

Reorder the terms:
-527 + 527 + 11q + q2 = 0 + 527

Combine like terms: -527 + 527 = 0
0 + 11q + q2 = 0 + 527
11q + q2 = 0 + 527

Combine like terms: 0 + 527 = 527
11q + q2 = 527

The q term is 11q.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11q + 30.25 + q2 = 527 + 30.25

Reorder the terms:
30.25 + 11q + q2 = 527 + 30.25

Combine like terms: 527 + 30.25 = 557.25
30.25 + 11q + q2 = 557.25

Factor a perfect square on the left side:
(q + 5.5)(q + 5.5) = 557.25

Calculate the square root of the right side: 23.606143268

Break this problem into two subproblems by setting 
(q + 5.5) equal to 23.606143268 and -23.606143268.


Subproblem 1
q + 5.5 = 23.606143268

Simplifying
q + 5.5 = 23.606143268

Reorder the terms:
5.5 + q = 23.606143268

Solving
5.5 + q = 23.606143268

Solving for variable 'q'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + q = 23.606143268 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + q = 23.606143268 + -5.5
q = 23.606143268 + -5.5

Combine like terms: 23.606143268 + -5.5 = 18.106143268
q = 18.106143268

Simplifying
q = 18.106143268


Subproblem 2
q + 5.5 = -23.606143268

Simplifying
q + 5.5 = -23.606143268

Reorder the terms:
5.5 + q = -23.606143268

Solving
5.5 + q = -23.606143268

Solving for variable 'q'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + q = -23.606143268 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + q = -23.606143268 + -5.5
q = -23.606143268 + -5.5

Combine like terms: -23.606143268 + -5.5 = -29.106143268
q = -29.106143268

Simplifying
q = -29.106143268


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {18.106143268, -29.106143268}
Solution
q = {18.106143268, -29.106143268}

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