4q^2+88q+92=0

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Solution for 4q^2+88q+92=0 equation: 


Simplifying
4q2 + 88q + 92 = 0

Reorder the terms:
92 + 88q + 4q2 = 0

Solving
92 + 88q + 4q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '4'.
4(23 + 22q + q2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(23 + 22q + q2)' equal to zero and attempt to solve:

Simplifying
23 + 22q + q2 = 0

Solving
23 + 22q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 22q + -23 + q2 = 0 + -23

Reorder the terms:
23 + -23 + 22q + q2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 22q + q2 = 0 + -23
22q + q2 = 0 + -23

Combine like terms: 0 + -23 = -23
22q + q2 = -23

The q term is 22q.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22q + 121 + q2 = -23 + 121

Reorder the terms:
121 + 22q + q2 = -23 + 121

Combine like terms: -23 + 121 = 98
121 + 22q + q2 = 98

Factor a perfect square on the left side:
(q + 11)(q + 11) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(q + 11) equal to 9.899494937 and -9.899494937.


Subproblem 1
q + 11 = 9.899494937

Simplifying
q + 11 = 9.899494937

Reorder the terms:
11 + q = 9.899494937

Solving
11 + q = 9.899494937

Solving for variable 'q'.

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

Add '-11' to each side of the equation.
11 + -11 + q = 9.899494937 + -11

Combine like terms: 11 + -11 = 0
0 + q = 9.899494937 + -11
q = 9.899494937 + -11

Combine like terms: 9.899494937 + -11 = -1.100505063
q = -1.100505063

Simplifying
q = -1.100505063


Subproblem 2
q + 11 = -9.899494937

Simplifying
q + 11 = -9.899494937

Reorder the terms:
11 + q = -9.899494937

Solving
11 + q = -9.899494937

Solving for variable 'q'.

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

Add '-11' to each side of the equation.
11 + -11 + q = -9.899494937 + -11

Combine like terms: 11 + -11 = 0
0 + q = -9.899494937 + -11
q = -9.899494937 + -11

Combine like terms: -9.899494937 + -11 = -20.899494937
q = -20.899494937

Simplifying
q = -20.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-1.100505063, -20.899494937}
Solution
q = {-1.100505063, -20.899494937}

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