a*a=(a*a*a*a)-(.5*4)

Solution for a*a=(a*a*a*a)-(.5*4) equation:

Simplifying
a * a = (a * a * a * a) + -1(0.5 * 4)

Multiply a * a
a2 = (a * a * a * a) + -1(0.5 * 4)

Multiply a * a
a2 = (a2 * a * a) + -1(0.5 * 4)

Multiply a2 * a
a2 = (a3 * a) + -1(0.5 * 4)

Multiply a3 * a
a2 = (a4) + -1(0.5 * 4)
a2 = a4 + -1(0.5 * 4)

Multiply 0.5 * 4
a2 = a4 + -1(2)

Multiply -1 * 2
a2 = a4 + -2

Reorder the terms:
a2 = -2 + a4

Solving
a2 = -2 + a4

Solving for variable 'a'.

Reorder the terms:
2 + a2 + -1a4 = -2 + a4 + 2 + -1a4

Reorder the terms:
2 + a2 + -1a4 = -2 + 2 + a4 + -1a4

Combine like terms: -2 + 2 = 0
2 + a2 + -1a4 = 0 + a4 + -1a4
2 + a2 + -1a4 = a4 + -1a4

Combine like terms: a4 + -1a4 = 0
2 + a2 + -1a4 = 0

Factor a trinomial.
(2 + -1a2)(1 + a2) = 0

Subproblem 1
Set the factor '(2 + -1a2)' equal to zero and attempt to solve:

Simplifying
2 + -1a2 = 0

Solving
2 + -1a2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a2 = 0 + -2
-1a2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1a2 = -2

Divide each side by '-1'.
a2 = 2

Simplifying
a2 = 2

Take the square root of each side:
a = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(1 + a2)' equal to zero and attempt to solve:

Simplifying
1 + a2 = 0

Solving
1 + a2 = 0

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

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

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

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

Simplifying
a2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {-1.414213562, 1.414213562}