A(A-5)=18

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Solution for A(A-5)=18 equation: 


Simplifying
A(A + -5) = 18

Reorder the terms:
A(-5 + A) = 18
(-5 * A + A * A) = 18
(-5A + A2) = 18

Solving
-5A + A2 = 18

Solving for variable 'A'.

Reorder the terms:
-18 + -5A + A2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -5A + A2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -5A + 18 + A2 = 0 + 18

Reorder the terms:
-18 + 18 + -5A + A2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -5A + A2 = 0 + 18
-5A + A2 = 0 + 18

Combine like terms: 0 + 18 = 18
-5A + A2 = 18

The A term is -5A.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5A + 6.25 + A2 = 18 + 6.25

Reorder the terms:
6.25 + -5A + A2 = 18 + 6.25

Combine like terms: 18 + 6.25 = 24.25
6.25 + -5A + A2 = 24.25

Factor a perfect square on the left side:
(A + -2.5)(A + -2.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(A + -2.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
A + -2.5 = 4.924428901

Simplifying
A + -2.5 = 4.924428901

Reorder the terms:
-2.5 + A = 4.924428901

Solving
-2.5 + A = 4.924428901

Solving for variable 'A'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + A = 4.924428901 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + A = 4.924428901 + 2.5
A = 4.924428901 + 2.5

Combine like terms: 4.924428901 + 2.5 = 7.424428901
A = 7.424428901

Simplifying
A = 7.424428901


Subproblem 2
A + -2.5 = -4.924428901

Simplifying
A + -2.5 = -4.924428901

Reorder the terms:
-2.5 + A = -4.924428901

Solving
-2.5 + A = -4.924428901

Solving for variable 'A'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + A = -4.924428901 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + A = -4.924428901 + 2.5
A = -4.924428901 + 2.5

Combine like terms: -4.924428901 + 2.5 = -2.424428901
A = -2.424428901

Simplifying
A = -2.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
A = {7.424428901, -2.424428901}

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