(a-26)a=(a-18)-35

Solution for (a-26)a=(a-18)-35 equation:

Simplifying
(a + -26) * a = (a + -18) + -35

Reorder the terms:
(-26 + a) * a = (a + -18) + -35

Reorder the terms for easier multiplication:
a(-26 + a) = (a + -18) + -35
(-26 * a + a * a) = (a + -18) + -35
(-26a + a2) = (a + -18) + -35

Reorder the terms:
-26a + a2 = (-18 + a) + -35

Remove parenthesis around (-18 + a)
-26a + a2 = -18 + a + -35

Reorder the terms:
-26a + a2 = -18 + -35 + a

Combine like terms: -18 + -35 = -53
-26a + a2 = -53 + a

Solving
-26a + a2 = -53 + a

Solving for variable 'a'.

Reorder the terms:
53 + -26a + -1a + a2 = -53 + a + 53 + -1a

Combine like terms: -26a + -1a = -27a
53 + -27a + a2 = -53 + a + 53 + -1a

Reorder the terms:
53 + -27a + a2 = -53 + 53 + a + -1a

Combine like terms: -53 + 53 = 0
53 + -27a + a2 = 0 + a + -1a
53 + -27a + a2 = a + -1a

Combine like terms: a + -1a = 0
53 + -27a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-53' to each side of the equation.
53 + -27a + -53 + a2 = 0 + -53

Reorder the terms:
53 + -53 + -27a + a2 = 0 + -53

Combine like terms: 53 + -53 = 0
0 + -27a + a2 = 0 + -53
-27a + a2 = 0 + -53

Combine like terms: 0 + -53 = -53
-27a + a2 = -53

The a term is -27a.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27a + 182.25 + a2 = -53 + 182.25

Reorder the terms:
182.25 + -27a + a2 = -53 + 182.25

Combine like terms: -53 + 182.25 = 129.25
182.25 + -27a + a2 = 129.25

Factor a perfect square on the left side:
(a + -13.5)(a + -13.5) = 129.25

Calculate the square root of the right side: 11.368817001

Break this problem into two subproblems by setting 
(a + -13.5) equal to 11.368817001 and -11.368817001.

Subproblem 1
a + -13.5 = 11.368817001

Simplifying
a + -13.5 = 11.368817001

Reorder the terms:
-13.5 + a = 11.368817001

Solving
-13.5 + a = 11.368817001

Solving for variable 'a'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + a = 11.368817001 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + a = 11.368817001 + 13.5
a = 11.368817001 + 13.5

Combine like terms: 11.368817001 + 13.5 = 24.868817001
a = 24.868817001

Simplifying
a = 24.868817001

Subproblem 2
a + -13.5 = -11.368817001

Simplifying
a + -13.5 = -11.368817001

Reorder the terms:
-13.5 + a = -11.368817001

Solving
-13.5 + a = -11.368817001

Solving for variable 'a'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + a = -11.368817001 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + a = -11.368817001 + 13.5
a = -11.368817001 + 13.5

Combine like terms: -11.368817001 + 13.5 = 2.131182999
a = 2.131182999

Simplifying
a = 2.131182999

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {24.868817001, 2.131182999}