q^2+17q+35=0

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Solution for q^2+17q+35=0 equation: 


Simplifying
q2 + 17q + 35 = 0

Reorder the terms:
35 + 17q + q2 = 0

Solving
35 + 17q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 17q + -35 + q2 = 0 + -35

Reorder the terms:
35 + -35 + 17q + q2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 17q + q2 = 0 + -35
17q + q2 = 0 + -35

Combine like terms: 0 + -35 = -35
17q + q2 = -35

The q term is 17q.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17q + 72.25 + q2 = -35 + 72.25

Reorder the terms:
72.25 + 17q + q2 = -35 + 72.25

Combine like terms: -35 + 72.25 = 37.25
72.25 + 17q + q2 = 37.25

Factor a perfect square on the left side:
(q + 8.5)(q + 8.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(q + 8.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
q + 8.5 = 6.103277808

Simplifying
q + 8.5 = 6.103277808

Reorder the terms:
8.5 + q = 6.103277808

Solving
8.5 + q = 6.103277808

Solving for variable 'q'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + q = 6.103277808 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + q = 6.103277808 + -8.5
q = 6.103277808 + -8.5

Combine like terms: 6.103277808 + -8.5 = -2.396722192
q = -2.396722192

Simplifying
q = -2.396722192


Subproblem 2
q + 8.5 = -6.103277808

Simplifying
q + 8.5 = -6.103277808

Reorder the terms:
8.5 + q = -6.103277808

Solving
8.5 + q = -6.103277808

Solving for variable 'q'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + q = -6.103277808 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + q = -6.103277808 + -8.5
q = -6.103277808 + -8.5

Combine like terms: -6.103277808 + -8.5 = -14.603277808
q = -14.603277808

Simplifying
q = -14.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-2.396722192, -14.603277808}

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