10-a=a*a

Solution for 10-a=a*a equation:

Simplifying
10 + -1a = a * a

Multiply a * a
10 + -1a = a2

Solving
10 + -1a = a2

Solving for variable 'a'.

Combine like terms: a2 + -1a2 = 0
10 + -1a + -1a2 = 0

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

Divide each side by '-1'.
-10 + a + a2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + a + a2 = 0 + 10
a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
a + a2 = 10

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + a2 = 10 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + a2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
1.25 + a2 = 10.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(a + 0.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
a + 0.5 = 3.201562119

Simplifying
a + 0.5 = 3.201562119

Reorder the terms:
0.5 + a = 3.201562119

Solving
0.5 + a = 3.201562119

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 3.201562119 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 3.201562119 + -0.5
a = 3.201562119 + -0.5

Combine like terms: 3.201562119 + -0.5 = 2.701562119
a = 2.701562119

Simplifying
a = 2.701562119

Subproblem 2
a + 0.5 = -3.201562119

Simplifying
a + 0.5 = -3.201562119

Reorder the terms:
0.5 + a = -3.201562119

Solving
0.5 + a = -3.201562119

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -3.201562119 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -3.201562119 + -0.5
a = -3.201562119 + -0.5

Combine like terms: -3.201562119 + -0.5 = -3.701562119
a = -3.701562119

Simplifying
a = -3.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.701562119, -3.701562119}