q^2-200q+540=0

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Solution for q^2-200q+540=0 equation: 


Simplifying
q2 + -200q + 540 = 0

Reorder the terms:
540 + -200q + q2 = 0

Solving
540 + -200q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-540' to each side of the equation.
540 + -200q + -540 + q2 = 0 + -540

Reorder the terms:
540 + -540 + -200q + q2 = 0 + -540

Combine like terms: 540 + -540 = 0
0 + -200q + q2 = 0 + -540
-200q + q2 = 0 + -540

Combine like terms: 0 + -540 = -540
-200q + q2 = -540

The q term is -200q.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200q + 10000 + q2 = -540 + 10000

Reorder the terms:
10000 + -200q + q2 = -540 + 10000

Combine like terms: -540 + 10000 = 9460
10000 + -200q + q2 = 9460

Factor a perfect square on the left side:
(q + -100)(q + -100) = 9460

Calculate the square root of the right side: 97.262531326

Break this problem into two subproblems by setting 
(q + -100) equal to 97.262531326 and -97.262531326.


Subproblem 1
q + -100 = 97.262531326

Simplifying
q + -100 = 97.262531326

Reorder the terms:
-100 + q = 97.262531326

Solving
-100 + q = 97.262531326

Solving for variable 'q'.

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

Add '100' to each side of the equation.
-100 + 100 + q = 97.262531326 + 100

Combine like terms: -100 + 100 = 0
0 + q = 97.262531326 + 100
q = 97.262531326 + 100

Combine like terms: 97.262531326 + 100 = 197.262531326
q = 197.262531326

Simplifying
q = 197.262531326


Subproblem 2
q + -100 = -97.262531326

Simplifying
q + -100 = -97.262531326

Reorder the terms:
-100 + q = -97.262531326

Solving
-100 + q = -97.262531326

Solving for variable 'q'.

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

Add '100' to each side of the equation.
-100 + 100 + q = -97.262531326 + 100

Combine like terms: -100 + 100 = 0
0 + q = -97.262531326 + 100
q = -97.262531326 + 100

Combine like terms: -97.262531326 + 100 = 2.737468674
q = 2.737468674

Simplifying
q = 2.737468674


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {197.262531326, 2.737468674}

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