-a(a)+a+400=0

Solution for -a(a)+a+400=0 equation:

Simplifying
-1a(a) + a + 400 = 0

Multiply a * a
-1a2 + a + 400 = 0

Reorder the terms:
400 + a + -1a2 = 0

Solving
400 + a + -1a2 = 0

Solving for variable 'a'.

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

Divide each side by '-1'.
-400 + -1a + a2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -1a + 400 + a2 = 0 + 400

Reorder the terms:
-400 + 400 + -1a + a2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -1a + a2 = 0 + 400
-1a + a2 = 0 + 400

Combine like terms: 0 + 400 = 400
-1a + a2 = 400

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.
-1a + 0.25 + a2 = 400 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 400 + 0.25

Combine like terms: 400 + 0.25 = 400.25
0.25 + -1a + a2 = 400.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 400.25

Calculate the square root of the right side: 20.006249024

Break this problem into two subproblems by setting 
(a + 0.5) equal to 20.006249024 and -20.006249024.

Subproblem 1
a + 0.5 = 20.006249024

Simplifying
a + 0.5 = 20.006249024

Reorder the terms:
0.5 + a = 20.006249024

Solving
0.5 + a = 20.006249024

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 = 20.006249024 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 20.006249024 + -0.5
a = 20.006249024 + -0.5

Combine like terms: 20.006249024 + -0.5 = 19.506249024
a = 19.506249024

Simplifying
a = 19.506249024

Subproblem 2
a + 0.5 = -20.006249024

Simplifying
a + 0.5 = -20.006249024

Reorder the terms:
0.5 + a = -20.006249024

Solving
0.5 + a = -20.006249024

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 = -20.006249024 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -20.006249024 + -0.5
a = -20.006249024 + -0.5

Combine like terms: -20.006249024 + -0.5 = -20.506249024
a = -20.506249024

Simplifying
a = -20.506249024

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {19.506249024, -20.506249024}