q^2+20q+47=0

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Solution for q^2+20q+47=0 equation: 


Simplifying
q2 + 20q + 47 = 0

Reorder the terms:
47 + 20q + q2 = 0

Solving
47 + 20q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + 20q + -47 + q2 = 0 + -47

Reorder the terms:
47 + -47 + 20q + q2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 20q + q2 = 0 + -47
20q + q2 = 0 + -47

Combine like terms: 0 + -47 = -47
20q + q2 = -47

The q term is 20q.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20q + 100 + q2 = -47 + 100

Reorder the terms:
100 + 20q + q2 = -47 + 100

Combine like terms: -47 + 100 = 53
100 + 20q + q2 = 53

Factor a perfect square on the left side:
(q + 10)(q + 10) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(q + 10) equal to 7.280109889 and -7.280109889.


Subproblem 1
q + 10 = 7.280109889

Simplifying
q + 10 = 7.280109889

Reorder the terms:
10 + q = 7.280109889

Solving
10 + q = 7.280109889

Solving for variable 'q'.

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

Add '-10' to each side of the equation.
10 + -10 + q = 7.280109889 + -10

Combine like terms: 10 + -10 = 0
0 + q = 7.280109889 + -10
q = 7.280109889 + -10

Combine like terms: 7.280109889 + -10 = -2.719890111
q = -2.719890111

Simplifying
q = -2.719890111


Subproblem 2
q + 10 = -7.280109889

Simplifying
q + 10 = -7.280109889

Reorder the terms:
10 + q = -7.280109889

Solving
10 + q = -7.280109889

Solving for variable 'q'.

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

Add '-10' to each side of the equation.
10 + -10 + q = -7.280109889 + -10

Combine like terms: 10 + -10 = 0
0 + q = -7.280109889 + -10
q = -7.280109889 + -10

Combine like terms: -7.280109889 + -10 = -17.280109889
q = -17.280109889

Simplifying
q = -17.280109889


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-2.719890111, -17.280109889}

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