q^2+30q+19=0

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Solution for q^2+30q+19=0 equation: 


Simplifying
q2 + 30q + 19 = 0

Reorder the terms:
19 + 30q + q2 = 0

Solving
19 + 30q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 30q + -19 + q2 = 0 + -19

Reorder the terms:
19 + -19 + 30q + q2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 30q + q2 = 0 + -19
30q + q2 = 0 + -19

Combine like terms: 0 + -19 = -19
30q + q2 = -19

The q term is 30q.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30q + 225 + q2 = -19 + 225

Reorder the terms:
225 + 30q + q2 = -19 + 225

Combine like terms: -19 + 225 = 206
225 + 30q + q2 = 206

Factor a perfect square on the left side:
(q + 15)(q + 15) = 206

Calculate the square root of the right side: 14.352700094

Break this problem into two subproblems by setting 
(q + 15) equal to 14.352700094 and -14.352700094.


Subproblem 1
q + 15 = 14.352700094

Simplifying
q + 15 = 14.352700094

Reorder the terms:
15 + q = 14.352700094

Solving
15 + q = 14.352700094

Solving for variable 'q'.

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

Add '-15' to each side of the equation.
15 + -15 + q = 14.352700094 + -15

Combine like terms: 15 + -15 = 0
0 + q = 14.352700094 + -15
q = 14.352700094 + -15

Combine like terms: 14.352700094 + -15 = -0.647299906
q = -0.647299906

Simplifying
q = -0.647299906


Subproblem 2
q + 15 = -14.352700094

Simplifying
q + 15 = -14.352700094

Reorder the terms:
15 + q = -14.352700094

Solving
15 + q = -14.352700094

Solving for variable 'q'.

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

Add '-15' to each side of the equation.
15 + -15 + q = -14.352700094 + -15

Combine like terms: 15 + -15 = 0
0 + q = -14.352700094 + -15
q = -14.352700094 + -15

Combine like terms: -14.352700094 + -15 = -29.352700094
q = -29.352700094

Simplifying
q = -29.352700094


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-0.647299906, -29.352700094}

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