q^2-10q-20=0

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Solution for q^2-10q-20=0 equation: 


Simplifying
q2 + -10q + -20 = 0

Reorder the terms:
-20 + -10q + q2 = 0

Solving
-20 + -10q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -10q + 20 + q2 = 0 + 20

Reorder the terms:
-20 + 20 + -10q + q2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -10q + q2 = 0 + 20
-10q + q2 = 0 + 20

Combine like terms: 0 + 20 = 20
-10q + q2 = 20

The q term is -10q.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10q + 25 + q2 = 20 + 25

Reorder the terms:
25 + -10q + q2 = 20 + 25

Combine like terms: 20 + 25 = 45
25 + -10q + q2 = 45

Factor a perfect square on the left side:
(q + -5)(q + -5) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(q + -5) equal to 6.708203933 and -6.708203933.


Subproblem 1
q + -5 = 6.708203933

Simplifying
q + -5 = 6.708203933

Reorder the terms:
-5 + q = 6.708203933

Solving
-5 + q = 6.708203933

Solving for variable 'q'.

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

Add '5' to each side of the equation.
-5 + 5 + q = 6.708203933 + 5

Combine like terms: -5 + 5 = 0
0 + q = 6.708203933 + 5
q = 6.708203933 + 5

Combine like terms: 6.708203933 + 5 = 11.708203933
q = 11.708203933

Simplifying
q = 11.708203933


Subproblem 2
q + -5 = -6.708203933

Simplifying
q + -5 = -6.708203933

Reorder the terms:
-5 + q = -6.708203933

Solving
-5 + q = -6.708203933

Solving for variable 'q'.

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

Add '5' to each side of the equation.
-5 + 5 + q = -6.708203933 + 5

Combine like terms: -5 + 5 = 0
0 + q = -6.708203933 + 5
q = -6.708203933 + 5

Combine like terms: -6.708203933 + 5 = -1.708203933
q = -1.708203933

Simplifying
q = -1.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {11.708203933, -1.708203933}

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