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

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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}

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