q^2+8q-2=0

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Solution for q^2+8q-2=0 equation: 


Simplifying
q2 + 8q + -2 = 0

Reorder the terms:
-2 + 8q + q2 = 0

Solving
-2 + 8q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8q + 2 + q2 = 0 + 2

Reorder the terms:
-2 + 2 + 8q + q2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8q + q2 = 0 + 2
8q + q2 = 0 + 2

Combine like terms: 0 + 2 = 2
8q + q2 = 2

The q term is 8q.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8q + 16 + q2 = 2 + 16

Reorder the terms:
16 + 8q + q2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + 8q + q2 = 18

Factor a perfect square on the left side:
(q + 4)(q + 4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(q + 4) equal to 4.242640687 and -4.242640687.


Subproblem 1
q + 4 = 4.242640687

Simplifying
q + 4 = 4.242640687

Reorder the terms:
4 + q = 4.242640687

Solving
4 + q = 4.242640687

Solving for variable 'q'.

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

Add '-4' to each side of the equation.
4 + -4 + q = 4.242640687 + -4

Combine like terms: 4 + -4 = 0
0 + q = 4.242640687 + -4
q = 4.242640687 + -4

Combine like terms: 4.242640687 + -4 = 0.242640687
q = 0.242640687

Simplifying
q = 0.242640687


Subproblem 2
q + 4 = -4.242640687

Simplifying
q + 4 = -4.242640687

Reorder the terms:
4 + q = -4.242640687

Solving
4 + q = -4.242640687

Solving for variable 'q'.

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

Add '-4' to each side of the equation.
4 + -4 + q = -4.242640687 + -4

Combine like terms: 4 + -4 = 0
0 + q = -4.242640687 + -4
q = -4.242640687 + -4

Combine like terms: -4.242640687 + -4 = -8.242640687
q = -8.242640687

Simplifying
q = -8.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.242640687, -8.242640687}

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