2*8=a(a-7)

Solution for 2*8=a(a-7) equation:

Simplifying
2 * 8 = a(a + -7)

Multiply 2 * 8
16 = a(a + -7)

Reorder the terms:
16 = a(-7 + a)
16 = (-7 * a + a * a)
16 = (-7a + a2)

Solving
16 = -7a + a2

Solving for variable 'a'.

Reorder the terms:
16 + 7a + -1a2 = -7a + 7a + a2 + -1a2

Combine like terms: -7a + 7a = 0
16 + 7a + -1a2 = 0 + a2 + -1a2
16 + 7a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
16 + 7a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + -7a + a2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -7a + 16 + a2 = 0 + 16

Reorder the terms:
-16 + 16 + -7a + a2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -7a + a2 = 0 + 16
-7a + a2 = 0 + 16

Combine like terms: 0 + 16 = 16
-7a + a2 = 16

The a term is -7a.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7a + 12.25 + a2 = 16 + 12.25

Reorder the terms:
12.25 + -7a + a2 = 16 + 12.25

Combine like terms: 16 + 12.25 = 28.25
12.25 + -7a + a2 = 28.25

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(a + -3.5) equal to 5.315072906 and -5.315072906.

Subproblem 1
a + -3.5 = 5.315072906

Simplifying
a + -3.5 = 5.315072906

Reorder the terms:
-3.5 + a = 5.315072906

Solving
-3.5 + a = 5.315072906

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = 5.315072906 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = 5.315072906 + 3.5
a = 5.315072906 + 3.5

Combine like terms: 5.315072906 + 3.5 = 8.815072906
a = 8.815072906

Simplifying
a = 8.815072906

Subproblem 2
a + -3.5 = -5.315072906

Simplifying
a + -3.5 = -5.315072906

Reorder the terms:
-3.5 + a = -5.315072906

Solving
-3.5 + a = -5.315072906

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = -5.315072906 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = -5.315072906 + 3.5
a = -5.315072906 + 3.5

Combine like terms: -5.315072906 + 3.5 = -1.815072906
a = -1.815072906

Simplifying
a = -1.815072906

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {8.815072906, -1.815072906}