65-5a=2a^2

Solution for 65-5a=2a^2 equation:

Simplifying
65 + -5a = 2a2

Solving
65 + -5a = 2a2

Solving for variable 'a'.

Combine like terms: 2a2 + -2a2 = 0
65 + -5a + -2a2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-32.5 + 2.5a + a2 = 0

Move the constant term to the right:

Add '32.5' to each side of the equation.
-32.5 + 2.5a + 32.5 + a2 = 0 + 32.5

Reorder the terms:
-32.5 + 32.5 + 2.5a + a2 = 0 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + 2.5a + a2 = 0 + 32.5
2.5a + a2 = 0 + 32.5

Combine like terms: 0 + 32.5 = 32.5
2.5a + a2 = 32.5

The a term is 2.5a.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5a + 1.5625 + a2 = 32.5 + 1.5625

Reorder the terms:
1.5625 + 2.5a + a2 = 32.5 + 1.5625

Combine like terms: 32.5 + 1.5625 = 34.0625
1.5625 + 2.5a + a2 = 34.0625

Factor a perfect square on the left side:
(a + 1.25)(a + 1.25) = 34.0625

Calculate the square root of the right side: 5.836308765

Break this problem into two subproblems by setting 
(a + 1.25) equal to 5.836308765 and -5.836308765.

Subproblem 1
a + 1.25 = 5.836308765

Simplifying
a + 1.25 = 5.836308765

Reorder the terms:
1.25 + a = 5.836308765

Solving
1.25 + a = 5.836308765

Solving for variable 'a'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + a = 5.836308765 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + a = 5.836308765 + -1.25
a = 5.836308765 + -1.25

Combine like terms: 5.836308765 + -1.25 = 4.586308765
a = 4.586308765

Simplifying
a = 4.586308765

Subproblem 2
a + 1.25 = -5.836308765

Simplifying
a + 1.25 = -5.836308765

Reorder the terms:
1.25 + a = -5.836308765

Solving
1.25 + a = -5.836308765

Solving for variable 'a'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + a = -5.836308765 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + a = -5.836308765 + -1.25
a = -5.836308765 + -1.25

Combine like terms: -5.836308765 + -1.25 = -7.086308765
a = -7.086308765

Simplifying
a = -7.086308765

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.586308765, -7.086308765}