A(A-21)-100=A

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Solution for A(A-21)-100=A equation: 


Simplifying
A(A + -21) + -100 = A

Reorder the terms:
A(-21 + A) + -100 = A
(-21 * A + A * A) + -100 = A
(-21A + A2) + -100 = A

Reorder the terms:
-100 + -21A + A2 = A

Solving
-100 + -21A + A2 = A

Solving for variable 'A'.

Reorder the terms:
-100 + -21A + -1A + A2 = A + -1A

Combine like terms: -21A + -1A = -22A
-100 + -22A + A2 = A + -1A

Combine like terms: A + -1A = 0
-100 + -22A + A2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -22A + 100 + A2 = 0 + 100

Reorder the terms:
-100 + 100 + -22A + A2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -22A + A2 = 0 + 100
-22A + A2 = 0 + 100

Combine like terms: 0 + 100 = 100
-22A + A2 = 100

The A term is -22A.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22A + 121 + A2 = 100 + 121

Reorder the terms:
121 + -22A + A2 = 100 + 121

Combine like terms: 100 + 121 = 221
121 + -22A + A2 = 221

Factor a perfect square on the left side:
(A + -11)(A + -11) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(A + -11) equal to 14.866068747 and -14.866068747.


Subproblem 1
A + -11 = 14.866068747

Simplifying
A + -11 = 14.866068747

Reorder the terms:
-11 + A = 14.866068747

Solving
-11 + A = 14.866068747

Solving for variable 'A'.

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

Add '11' to each side of the equation.
-11 + 11 + A = 14.866068747 + 11

Combine like terms: -11 + 11 = 0
0 + A = 14.866068747 + 11
A = 14.866068747 + 11

Combine like terms: 14.866068747 + 11 = 25.866068747
A = 25.866068747

Simplifying
A = 25.866068747


Subproblem 2
A + -11 = -14.866068747

Simplifying
A + -11 = -14.866068747

Reorder the terms:
-11 + A = -14.866068747

Solving
-11 + A = -14.866068747

Solving for variable 'A'.

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

Add '11' to each side of the equation.
-11 + 11 + A = -14.866068747 + 11

Combine like terms: -11 + 11 = 0
0 + A = -14.866068747 + 11
A = -14.866068747 + 11

Combine like terms: -14.866068747 + 11 = -3.866068747
A = -3.866068747

Simplifying
A = -3.866068747


Solution
The solution to the problem is based on the solutions
from the subproblems.
A = {25.866068747, -3.866068747}

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