A(A-21)=11

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Solution for A(A-21)=11 equation: 


Simplifying
A(A + -21) = 11

Reorder the terms:
A(-21 + A) = 11
(-21 * A + A * A) = 11
(-21A + A2) = 11

Solving
-21A + A2 = 11

Solving for variable 'A'.

Reorder the terms:
-11 + -21A + A2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -21A + A2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -21A + 11 + A2 = 0 + 11

Reorder the terms:
-11 + 11 + -21A + A2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -21A + A2 = 0 + 11
-21A + A2 = 0 + 11

Combine like terms: 0 + 11 = 11
-21A + A2 = 11

The A term is -21A.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21A + 110.25 + A2 = 11 + 110.25

Reorder the terms:
110.25 + -21A + A2 = 11 + 110.25

Combine like terms: 11 + 110.25 = 121.25
110.25 + -21A + A2 = 121.25

Factor a perfect square on the left side:
(A + -10.5)(A + -10.5) = 121.25

Calculate the square root of the right side: 11.011357773

Break this problem into two subproblems by setting 
(A + -10.5) equal to 11.011357773 and -11.011357773.


Subproblem 1
A + -10.5 = 11.011357773

Simplifying
A + -10.5 = 11.011357773

Reorder the terms:
-10.5 + A = 11.011357773

Solving
-10.5 + A = 11.011357773

Solving for variable 'A'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + A = 11.011357773 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + A = 11.011357773 + 10.5
A = 11.011357773 + 10.5

Combine like terms: 11.011357773 + 10.5 = 21.511357773
A = 21.511357773

Simplifying
A = 21.511357773


Subproblem 2
A + -10.5 = -11.011357773

Simplifying
A + -10.5 = -11.011357773

Reorder the terms:
-10.5 + A = -11.011357773

Solving
-10.5 + A = -11.011357773

Solving for variable 'A'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + A = -11.011357773 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + A = -11.011357773 + 10.5
A = -11.011357773 + 10.5

Combine like terms: -11.011357773 + 10.5 = -0.511357773
A = -0.511357773

Simplifying
A = -0.511357773


Solution
The solution to the problem is based on the solutions
from the subproblems.
A = {21.511357773, -0.511357773}

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