q^2-20q-43=0

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Solution for q^2-20q-43=0 equation: 


Simplifying
q2 + -20q + -43 = 0

Reorder the terms:
-43 + -20q + q2 = 0

Solving
-43 + -20q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -20q + 43 + q2 = 0 + 43

Reorder the terms:
-43 + 43 + -20q + q2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -20q + q2 = 0 + 43
-20q + q2 = 0 + 43

Combine like terms: 0 + 43 = 43
-20q + q2 = 43

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 = 43 + 100

Reorder the terms:
100 + -20q + q2 = 43 + 100

Combine like terms: 43 + 100 = 143
100 + -20q + q2 = 143

Factor a perfect square on the left side:
(q + -10)(q + -10) = 143

Calculate the square root of the right side: 11.958260743

Break this problem into two subproblems by setting 
(q + -10) equal to 11.958260743 and -11.958260743.


Subproblem 1
q + -10 = 11.958260743

Simplifying
q + -10 = 11.958260743

Reorder the terms:
-10 + q = 11.958260743

Solving
-10 + q = 11.958260743

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 = 11.958260743 + 10

Combine like terms: -10 + 10 = 0
0 + q = 11.958260743 + 10
q = 11.958260743 + 10

Combine like terms: 11.958260743 + 10 = 21.958260743
q = 21.958260743

Simplifying
q = 21.958260743


Subproblem 2
q + -10 = -11.958260743

Simplifying
q + -10 = -11.958260743

Reorder the terms:
-10 + q = -11.958260743

Solving
-10 + q = -11.958260743

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 = -11.958260743 + 10

Combine like terms: -10 + 10 = 0
0 + q = -11.958260743 + 10
q = -11.958260743 + 10

Combine like terms: -11.958260743 + 10 = -1.958260743
q = -1.958260743

Simplifying
q = -1.958260743


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {21.958260743, -1.958260743}

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